I’m a 67 year old man who has forgotten many math concepts since high school and college. Thank you for your classes, as I have started to view one of your UA-cam classes every day. Great refresher!
@@vincewidemann868 exactly. Depending on common usage, many times in the field that gets mixed up. In a more clinical setting, I suppose not, but not everyone tells them apart.
I went at it looking for the height of the triangle by using half base x height = area. I took this approach as half base and height are equal in this case and the area of the triangle is half that of the square. Area of square = 1600, area of triangle = 800, square root of 800 = 28.28
approximately 28.28'. 40 / 2 = 20' to the center of one wall and another 20' to the center of the room. need to find the hypotenuse of 45,90,45 triangle. inverse sine of 45deg. = 1.414. 1.414 * 20' = 28.28'
I just cut a diagonal from corner to corner, making a right triangle and then use the Pythagorean Theorem. 40 squared = 1600 (2) = 3200. Square root of 3200 = 56.56/2 = 28.28. Oh, I didn't watch the video. Dude takes a 90 second problem and turns it into 20 minutes.
AI Grok says: The distance from the corner of a square room to the center is the length of the room's diagonal. For a square room with sides of length 40 feet, the diagonal is calculated using the Pythagorean theorem (a² + b² = c²). If a = b = 40, then: c² = a² + b² c² = 40² + 40² c² = 1600 + 1600 c² = 3200 c = √3200 c ≈ 56.57 So, the distance from the corner of the room to the center is approximately 56.57 feet.
40^2=1600 The diagonal is therefore √3200 Distance to the centre of the room is therefore half that, or 56.6÷2=28.3'. However, you have to allow for the space the you've occupied in the corner so it will be exactly 28' from your retina. Maybe.
I am a homeschooling mom to two teenage boys, and we thoroughly enjoy watching your videos as brainteasers/problem solving strategy games. I am going to humbly report that we interpreted your original wording to mean the room was 40 sq. foot. (As is sometimes written shorthand as 40 ft.^2) So we solved the problem with an 8 ft. by 5 ft. room. I believe your wording might be a bit ambiguous to others as well.
I almost made the same mistake.. but then I compared 40 ft sq room to 40 sq ft room. Not the same thing even if some people write it incorrectly. This is a Math Prof and he would definitely write it the correct way.
I had the same problem with the grammatic wording of the question. Was it a room with an area of 40 square ft. or a square shaped room, 40 ft on a side? Writing the question correctly would make it easier to answer. @@lindastrang8703
40 ft square room, means a room with walls that are 40 linear feet long. (40 ft square room) is not the same as a (40 square foot room). Finding the center distanced of 40 ft square room is easy if you know how. 40 sq ft room/area can be (1x40, 2x20, 4x10, 5x8). Find the center? I have never seen your short hand 40 ft.^2 in my life. I have been reading blueprints from many fields since I was 9 years old. I hope this helps.
@skim… That is reasonable notation, but the problem is kinda about grammar. Square is the adjective of what noun? To some extent though, from a homeschool perspective, if you’re analyzing a problem and using an appropriate analysis, that’s still good schooling. You are correct that these problems always have a potential ambiguity. That’s a potential first step. Even before trying to solve the problem, try to figure out what will the ambiguity be? That’s also a good test taking technique, identifying the twist that they are going to try tripping you up on.
Divide 40 by .707 that gives you corner to corner. Then divide that by 2. I used to use this laying out 45 degree corners in partitions when the length of the 45 Degree was given. Multiply by .707 gives you how far to measure from the 90 degree corner each way to create the 45 degree corner at the length given.
Some people cannot read. If he is laying out the walls then he needs the position not just the measurement therefore he is totally correct to draw the diagonal and divide by 2. It is also the correct answer to the problem posted using applied as opposed to pure maths
wait , halfway is 20 ft then 20 ft over so 20 squared + 20 squared = hypotnuse squared , so 400 + 400 = h suared , suare root or 800 =h ,or about 28 ft
With a 40 square, the sides are the square root of 40 = 6,32. Since we have a square the corners are 90 degrees. we have a right angle with two sides of 6,32. We can then find the diagonal of this right angle triangle by using Pythagoras. (6.32)^2 +(6.32)^2 equals the the square of the diagonal (80). And the square root of 80 is 8.94. And we only want half way across the diagonal so we divive by 2. =4,47.
What is interesting is you can skip the square root of 40 since you are going to be squaring it. So its 40 plus 40. 80. half the square root of 80. 4.47 feet.
@@robertthomas5906 " there is no way it's 4.47." Yes way. If the square contained 40 then the distance from corner to center is 4.47. If the EDGE measures 40 then the distance is 0.5 * sqrt( 40^2 + 40^2) Pythagorean Theorem]
@@thomasmaughan4798 You still did it wrong. Again, look at the video. He tells you. 40^2+40^2 is 1600+1600=3200. Sqrt of 3200 is 56.56. Half of that is.... not 4.47. It's 28.28. Which is why I said there is no way it's 4.47. That's because by inspection your 4.47, call it 5 would double to 10 and 10^2 is 100. Still way to short for the two sides. So it can't be 4.47. Remember, you in the corner of the room. You want the distance to the center. I'm not sure what you're figuring out it's so wrong. I couldn't give you even partial credit.
@@robertthomas5906 "You still did it wrong" THERE IS NO WRONG. There is only different and sometimes correct and incorrect. Right and wrong are moral judgments; correct and incorrect apply to methods. These videos take advantage of (1) different readings of English combined with (2) a common human desire to label someone else as wrong (not just incorrect).
Understood at minute 11:00 with the formula you reminded me of which was stored in some corner of my memory. ;) 1600 (a square) +1600 (b square) = 3200 3200 = C square Square root of 3200 = 56.26 The hypotenuse "C" is then 56.26 long. Divided by 2 = 28.28 OK! I am ready to work on my geometry now. It's been a while. I was hesitant to get back into geometry but your video gave me confidence to refresh my knowledge about that part of mathematics. And you reminded us the part about looking for a positive because we are talking about distance. Even better with the short cut formula that was also sleeping in some corner of my brain. Well explained Mr Math Man. :)
Multiply the length of the side by 1.414 to give you the length of the side opposite the right angle. i.e., 40 x 1.414 = 56.56. So you can multiply any number by 1.414 to give you the length of the side opposite the right angle.
Love your videos but found it way easier to make a right triangle at the half way point of the square and figure out the length of the long side with (2) 20' sides.
My, oh my, that was REALLY mucking about in the mumbo jumbo. Why not just multiply the sine of 45 degrees by the hypotenuse? One step instead of three. You should be making videos on making math more complicated than it really is, just like John.
Pythagorus (maybe, according to recent news articles) says the square of the hypotenuse is equal to the sum of the squares of the other 2 sides. So: 40 squared plus 40 squared = 3200 Square root of 3200 divided by 2 = 28.28 (to 2 decimal places)
Ancient architects must have understood this, if not in a purely mathematical sense. I'm sure that the 3-4-5 building square must have been used. Even so, the proof is easy if done graphically/empirically. They must have understood squares, if not square roots. After all, they were just as intelligent as modern day humans. We often underestimate them. They probably just thought differently. I often wonder how the Romans designed buildings using Roman numerals. I've tried doing mathematics with them but failed miserably.
I was a carpenter, so math was about 50% of my job. Here is a shorter more direct way. 40*1.414/2. 1.414 is the diagonal measurement of a 1" square. This came from my math book during my apprenticeship. This will only work on a perfect square.
As long as it is a square, there is a very simple way of getting the answer. You just need to know that the square root of 2 is 1.414. From that value all you need is the 4. Start by multiplying 40 x 4 then shift the decimal one place to the left. 40 x 4 = 160 --> 16.0 40+16=56 Now take the 56 and shift the decimal 2 more places to the left. 56 --> 0.56 Now add them together 56+0.56=56.56 Now you have the length of the hypotenuse but the question is how far to the center so half of 56.56 is 28.28 Enjoy!!
A really Simple way of figuring this out is, "What is the Square root of 800?" Since the square consists four Equilateral right angle triangles, each with a hypotenuse of 40'. Using Pythagoras we know that the square of the Hypotenuse = the sum of the square of the other two sides, so 40 x 40 = 1600, half of 1600 = 800, Sqrt of 800=28.28
No such thing as an equilateral right triangle. No equilateral triangle is a right triangle, Grasshopper. If we use "equilateral" literally, all three sides would be of equal length, which is impossible in a right triangle. A square is an equilateral rectangle. Use the Law of Sines and you'll see what I mean.
The first thing I did was to verify 40 foot square vs 40 square foot. Second I know a 45-45-90 triangle the hypotenuse is 1.414 of the shorter sides. Third short side is 40/2 = 20 feet * 1.414 = 28.28.
I got confused by 40' square. I questioned whether it meant 40' perimeter. Or 40 square feet. I figured the answer was either half of the square root of 200 or half of the square root of 40. I was always challenging the wording of problems.
The first step in this problem is getting the professor to clarify. Poorly worded problems like this and NOT clarifying are the difference between landing a rover on Mars and crashing a rover into Mars.
An isoceles right triangle (45,45,90) has sides of a,a,a*sqrt2. The right triangle formed with the hypotenuse from a corner to the center of a 40' square is a special triangle with sides of 20, 20 and 20*sqrt2, or 28 1/7.
¿Could you also just do sqrt(20^2+20^2) or 20 * sqrt(2), since you know half the distance of any side is 20 feet and it's 20 feet from the center of any wall to the middle, or because the sides are a nice even multiple of 10 you could do sqrt(2^2+2^2) * 10?
Yeah, I did it as 2x^2 = 1600, where the side of the room is the hypotenuse. Solving for x gives 20 * sqrt(2). It would have been cool if he showed both methods. It's a great way to demonstrate the beauty of math, how two different paths lead to the same destination. Like how you can derive the formula for the volume of a solid by doing different integrations.
My immediate approach: Center of one side(20), up to center of square(20). A2’d(400)+B2’d(400)= C2’d(800). Corner to center(hypotenuse) = sq root of 800, 28.28.
Here's another, slightly different, way to visualize it: If you draw two diagonal lines across the square, they meet in the center at 90 degrees. Now you have four right triangles, each on of which has the side of the square as the hypotenuse. The distance from the corner to the center is the length of the triangles' minor sides (which are all equal). The Pythagorean Theorem tells us that the length is the square root of one-half of the square of the hypotenuse. 40 x 40 = 1600; 1600/2 = 800; the square root of 800 is 20 radical 2.
Since it's a square, the two diagonals will, as well as intersecting at the centre, intersect at 90°. Thus, we have four isosceles, right-angle triangles, each with a 40' hypotenuse. Let 20' equal 1 JOE (a random linear unit of measurement) Therefore, each semi-diagonal is sqrt((2^2)÷2), or, sqrt 2. Which is 1.414 JOES Thus the distance to the centre from the corner is 1.414 x 20' = 28.28'. No calculator or pencil/paper required. But a knowledge of basic square roots is necessary. Later--- I chose 2 for the length of the hypotenuse because I happened to know that sqrt2 is 1.414 without calculating or looking it up.
28' 3 7/16ths" (I think,,) (no calculator) I'm a carpenter, I square up foundation and house walls routinely. 3,4,5 triangle is the 'go to' solver on most jobsites.
When I was about 7 years old, Johnny Mercer and Danny Kaye taught me, "The square of the hypotenuse of a right triangle is equal to the sum of the squares of the two adjacent sides." My methodology for solving this problem was a little different from yours, though. I bisected one of the right angles of the square, then bisected an adjacent right angle. This provided an isosceles triangle with two 45 degree angles (the two bisected 90 degree angles) leaving a right angle opposite the 40' hypotenuse of the created triangle. I know the two sides adjacent to the hypotenuse are equal, as their opposing angles are equal. Therefore, 2*x**2 (two x-squared) = 1600 (40 squared). X becomes the square root of 800, (using a calculator to compute the square root of 800) or approximately 28.28
When a shape is described as "X Square" generally means that the shape is a square, with dimensions of "X" being both length and width. If he was talking area, he would have written it out as 40 square foot.
28.28' The hypotenuse of an isocelese right triangle with sides of 1 would be the square root of 2, or 1.414. then by similar triangles you multiply that times 20. Calculator no es necessario.
I am just after the point of the video where you gave the answer, and my answer is correct. But I think i may have gotten the answer differently. Since it is a 40x40 room. I broke it up into 4 45° right triangles. Then using the calculator, I took 40 ÷√2 and got 28.28427124. Now this will only work on a square area. Now i will watch the rest of the video.
An angle will always be larger than side to side measuring. We quilters cut up fabric all the time and sew it back together. A half square triangle will be larger than half a square. A circle cut will also be larger, like a pizza, again an angle.
"A" squared plus "B" squared equals "C" square. A =40, B=40 thus 1600+1600=3200; C squared = 3200, c= 56.5685425. The center of room is half that so 28.2842712
28.28 feet. Since it is a square, there are right angles in the corners. the hypotenuse of two sides is 40 sq + 40 sq = Hypotenuse sq. the hypotenuse is the sq root of 3200, or 56.56 One half of that is the distance to the center.
If you draw a diagonal then you have a right triangle with two equal sides so the length of the diagonal is 40 times the square root of 2. To the center of the room is half this length so 20 times the square root of 2 or approximately 28.3 feet.
Square is 40’ per side. A person at a corner will walk along the diagonal half way from one corner to the opposite diagonal corner. Using a right triangle to represent this approximately 28.3’
A square room .. 40 x 40 .. and you want the distance from a corner to the centre. To get the distance from one corner to the opposite one think of a right angle triangle. The square of the distance from one corner to another = 40 squared + 40 squared X squared = 1600 + 1600 = 3200 The distance from one corner to another is the square root of 3200 and then you want half of that, but I don't have a calulator on me to do the square root bit !!
A handy way is to consider the general properties of a square is to consider the simplest length of a side as unit length 1. Therefore the diagonal length, by Pythagoras’ theorem is the square root of (1 squared (=1) plus 1 squared (=1), i.e. (1+1 =2). So the diagonal of our simple square is the square root of 2. Tip: If there is one square root to remember it is the square root of 2; i.e. = 1.414 (quite a neat number isn’t it?). Now, a 40 foot square room (not 40 square-foot room) has each side 40 feet. Divide it in half because the centre of the room lies on a parallel line half way along the side (i.e. 20feet) and Multiply 20 by our general diagonal - the square root of 2 i.e. (2x1.414); therefore the centre of the room is 28.28 feet from the corner.
Funny, I envisioned it as 40' being the hypotenuse, the length of the wall. The other two legs I envisioned as extending from each corner to the center. So my formula was 2Asquared = 40 squared. On further thought, I also saw it as A and B being 20', one half of the length of the wall with the hypotenuse running from the corner to the center of the room. Odd I never envisioned it as described in the video.
So right. I also commented on two previous examples which gave an incorrect answer for the problem posed. You want a precise answer, then ask a precise question.
28.28 feet I took the square root of 2 (1.414) and multiplied it by 40, then I divided that answer by two in order to find center. Any years of being a machinist has taught me some shortcuts for math. 40 x 1.414/2 = 28.28
My method was totally different, same answer. Not sure even how you arrived at that. I just used a triangle of 20 x 20. Not even like the example demonstrated.
half the room diagonal triangle from centre to another corner you still have 45, 45, 90 triangle, but now hypotenuse is 40. sin and cos 45 deg is 0.707, 0.707x 40 = 28.28
Easier to go 20’ down one side from the corner and then from that point perpendicular to the side then front thatpoint 20’ to the center. You now have a right triangle with 2 equal length sides. With these triangles the hypotenuse is equal to the square root of 2 times the length of a side. Which I’m sure you know. Like the videos, I’m what you call old school. Graduated HS in 64 and college in engineering In 69.
The mathematical calculation comes out to the square root of 800. However, that assumes you are standing right on the corner of the room, which is impossible. I'm not a ghost nor can I phase through matter. So, since my feet are 11 inches long and ther will be 2 inches between my heel and the actual corner, the the distance to the center of the room is sqrt(800)-11"-2" 28.28'-11"-2" (28.28×12)-13 339.42"-13" 321.42" or 27.2'
I read the question as a 40 square feet room (as opposed to your square room with 40’ sides)which threw me off. I couldn’t figure out the sides: 5’ x 8’ for example? This is why I failed math in high school I guess. I never read the questions correctly, lol 😂
Or. You could just multiply the side by .7 because your shop teacher/math teacher had you memorize that the diagonal of a square is 1.4 x the side. A sailor would also know that 1.4 times the distance up wind is the minimum amount you will have to sail to reach the weather mark.
On the bright side, I knew to go to A^2 + B^2 = C^2, 40^2 = 1600, 1600* 2 = 3200. I just didn't know square root of 3200 in my head, closest I got was just under 60 feet. Half of that would mean just under 30 feet.
I found something new how to measure any distance with a square. all you needs is a sight on the right side and on the left side a sight on a slide bar on the left side and a tape measure a crossed the top. With a 10 foot square you could easily measure the distance to the moon or sun in feet. I would like to discus this with table class math. I think this is how they did it thousands of years ago before Algebra or trig.
A (40ft) squared plus B (40ft) squared = C squared. 40x40 = 1600 + 1600 = 3200 The square root of which is 56.56 divided by two (half the distance from corner to corner) = 28.28 (your answer)
Is the 4O feet 10 * 4 40*4 1 side or all 4 I would use Pythagorean theorem. I love the problems that the 3,4,5 rule jump out of easy to do with out a calculator. This isn’t one of those.
Author didn't use a precise description of the area in question in the header: But assuming a 40 square foot square room; each side = 6.32 sq ft . In a corner, you'd be looking at a diagonal to the center. Using Pythagoras, diagonal works out to 8.93, center would be half the length of the diagonal or about 4.46 away from the corner. Of course the author assumed a square of 40 linear feet on each side. Answer is about 28.28.
I remember this from construction jobs when laying out building lines. A squared plus B squared equals C squared(the diagonal) then I took half of C to get the answer.
A 40' square room is either a room that has an area of 40 square feet, meaning that each of its sides are much shorter than 40 feet, given that they're a square root of 40, or the room is 40 square feet, but then it's no longer a square room. You've raised a contradiction and then changed the actual terms of the question by using 40 feet as the room's length and width, which then renders the room to be much larger than just 40 square feet. Which is it then?
I took it to be a forty foot square (i.e., a "room of forty square feet"). Reading comprehension (or lack thereof) strikes again, so of course I got the wrong answer. I used to do this all the time on math tests; use the proper procedure but misinterpret the instructions.
I reread the problem as he states in oh so many videos, a 40 ft square room is very, very different than a 40 square foot room. People are adding in words that are not in the problem. First read through, I did the same thing of thinking 40 sq ft, but that didn't make sense as NO room dimensions were given, thus the reread.
Yeah, I noticed the lack of dimensions and the distance from corner to center differs greatly if its 2 * sqrt(10) by 2 * sqrt(10), versus 1 ft by 40 ft.
I had to do a double take on the wording as well. If this were a test question, some of the students would answer this differently because of interpretation. The unfortunate problem is that these students would be punished (with their grade) even if their mathematical methodology was spot on. Yes, interpretation is very important, but wording ambiguity can nullify the effect of an otherwise good math question. I do believe that the question could be worded in a way that is far more clear. Example: You have a square room with a side that is 40 feet long, what is the measurement from the center of the room to one of the corners?
@@MathematicPlumber Just because wording requires analytical interpretation to understand correctly does not mean it is ambiguous. Wording it as "a square room with 40 foot sides" breeds lazy thinking.
Didn't watch the video. I don't know why it takes 22mins to explain this. Old mate Pythagoras is probably the only thing I remember from my school days nearly half a century ago. "Square of the hypoteneuse is equal to the sum of the squares of the other two sides." 40x40=1600. 1600 +1600=3200. √3200=56.56 (rounded). Centre is halfway along, so 28.28ft. Then i just skipped to the end to see if you got it right. Now, back to watching cat videos.
I solved this in my head in less than a minute, because I know that a 1 x 1 square has a diagonal of the square root of two, by Pythagorean. So its just a 20x20 square to reach from the corner to the middle, so 20 times the square root of 2.
Bad worded question is right!! I read it as 40' room that is square.(40x40 & 56.57 hypotenuse (28.285 to the center)) instead of, like it says a room with 40 ft² ie . 4x10, 2x20, 5x8...etc.(5.39,3.32,4.72 to the center) BTW. A square room that's 40ft ² has measurements of 6'4" X 6'4" and is 5'4⅔" from corner to center.😊 (P.S. I have a 40 sqft guest bathroom and the toilet is in the shower stall )
Well, I assumed it wasn't 40 Sq ft, but that left me with the problem of deciding whether each side was 40 ft, or the sum of sides were 40 ft - as both could be described as a 40 ft square room. Also left unknown was the height of said room. One assumes it's Flatland, as the room is a square, not a cube - but in Flatland it's a line, not a square. Are you sure we're in a room? Can't the room be omitted as unrelated data? Sigh - it's too early for such issues. I'll say it's 8 steps and let you calculate my height 😊
Judging solely by the question that's initially displayed (i.e. haven't watched the video), I would need some clarification due to the way it's worded. Does it mean it's a square room that's 40 ft on each side or does it mean that it's a 40 sq ft room?
So, I read this as a 40 sq feet room. As the area of the room was 40 square feet. 😅 I had to start watching the video to get a grip on it, and then I realized it is a 40 feet on a side. Sometimes I share this videos with my 14 years old grandson. But, I think I will share daily . 😊
When I hear 40 foot square room, I'm thinking a room that has 40 square feet, which means each wall would be about 6. 32 feet in length. which would make it about 4.46 feet to the center of the room, from a corner. or 53.5 inches. LOL (a small walkin closet. LOL)
John -- your math question wording is not as precise as we've come to expect. I first assumed it was a room 40 ft² (assumed a square) which meant, corner to center is 2•√10 or about 6.324 feet or just under 6ft 4 inches. With the size of the human body, you're about 5 feet away (assuming it's square). But if the room is a square room 40 feet per side then center to corner is √800 or 20√2. That comes out to 28.284 feet or just over 28 ft three inches. With the average size of the human body your face is about 27 feet away. "You are in a square room with sides 40 feet each. You want to install a bar (string/clothes line/something straight) from the corner to the center. How long will the bar (or whatever) have to be?"
just a note to the teacher: 'a 40 feet squeare room' means the area of the room is 40 feet .. maby be clearer in the future... assuming one side is 40 feet .. the math ppl presented r okay... (and as this isent advance math other options are omitted)
It's easy to do, all too often people incorrectly say feet squared when they mean square feet. I had to presume a math instructor would use the correct terminology.
Excellent. I'd forgotten about the sqrt of 2. Used it in plumbing to get the size of a copper tube running at 45 degrees to the next. 1.414. Guy working with me said, "What the hell you doing?" I looked like Einstein. So funny. All great videos.
I’m a 67 year old man who has forgotten many math concepts since high school and college. Thank you for your classes, as I have started to view one of your UA-cam classes every day. Great refresher!
Interpretation is everything. A 40'sq room can also be taken as a 5'x8' or 4'x10' room, being 40' square.
The difference being that one is 40 square feet and the other is a 40’ square.
@@vincewidemann868 exactly. Depending on common usage, many times in the field that gets mixed up. In a more clinical setting, I suppose not, but not everyone tells them apart.
It's 40 ft square room not 40 square feet. don't get confused
Then distance to the center of the room has no answer. Thus it has to be 40' x 40'.
I went at it looking for the height of the triangle by using half base x height = area. I took this approach as half base and height are equal in this case and the area of the triangle is half that of the square. Area of square = 1600, area of triangle = 800, square root of 800 = 28.28
approximately 28.28'. 40 / 2 = 20' to the center of one wall and another 20' to the center of the room. need to find the hypotenuse of 45,90,45 triangle. inverse sine of 45deg. = 1.414. 1.414 * 20' = 28.28'
I just cut a diagonal from corner to corner, making a right triangle and then use the Pythagorean Theorem. 40 squared = 1600 (2) = 3200. Square root of 3200 = 56.56/2 = 28.28. Oh, I didn't watch the video. Dude takes a 90 second problem and turns it into 20 minutes.
AI Grok says: The distance from the corner of a square room to the center is the length of the room's diagonal. For a square room with sides of length 40 feet, the diagonal is calculated using the Pythagorean theorem (a² + b² = c²).
If a = b = 40, then:
c² = a² + b²
c² = 40² + 40²
c² = 1600 + 1600
c² = 3200
c = √3200
c ≈ 56.57
So, the distance from the corner of the room to the center is approximately 56.57 feet.
Half of 56.57
40^2=1600
The diagonal is therefore √3200
Distance to the centre of the room is therefore half that, or 56.6÷2=28.3'.
However, you have to allow for the space the you've occupied in the corner so it will be exactly 28' from your retina. Maybe.
You are correct sir
I am a homeschooling mom to two teenage boys, and we thoroughly enjoy watching your videos as brainteasers/problem solving strategy games. I am going to humbly report that we interpreted your original wording to mean the room was 40 sq. foot. (As is sometimes written shorthand as 40 ft.^2) So we solved the problem with an 8 ft. by 5 ft. room. I believe your wording might be a bit ambiguous to others as well.
I almost made the same mistake.. but then I compared 40 ft sq room to 40 sq ft room. Not the same thing even if some people write it incorrectly. This is a Math Prof and he would definitely write it the correct way.
Agreed, his wording can be interpreted a few different ways.
I had the same problem with the grammatic wording of the question. Was it a room with an area of 40 square ft. or a square shaped room, 40 ft on a side? Writing the question correctly would make it easier to answer.
@@lindastrang8703
40 ft square room, means a room with walls that are 40 linear feet long. (40 ft square room) is not the same as a (40 square foot room). Finding the center distanced of 40 ft square room is easy if you know how. 40 sq ft room/area can be (1x40, 2x20, 4x10, 5x8). Find the center? I have never seen your short hand 40 ft.^2 in my life. I have been reading blueprints from many fields since I was 9 years old. I hope this helps.
@skim… That is reasonable notation, but the problem is kinda about grammar. Square is the adjective of what noun?
To some extent though, from a homeschool perspective, if you’re analyzing a problem and using an appropriate analysis, that’s still good schooling.
You are correct that these problems always have a potential ambiguity. That’s a potential first step. Even before trying to solve the problem, try to figure out what will the ambiguity be? That’s also a good test taking technique, identifying the twist that they are going to try tripping you up on.
Divide 40 by .707 that gives you corner to corner. Then divide that by 2. I used to use this laying out 45 degree corners in partitions when the length of the 45 Degree was given. Multiply by .707 gives you how far to measure from the 90 degree corner each way to create the 45 degree corner at the length given.
Just multiply 40 by 0.707 :/
.707 is the sine of 45 degrees, multiply that by one of the sides and you get 28.28. No need to divide 40 by .707, then divide by 2.
Some people cannot read. If he is laying out the walls then he needs the position not just the measurement therefore he is totally correct to draw the diagonal and divide by 2. It is also the correct answer to the problem posted using applied as opposed to pure maths
wait , halfway is 20 ft then 20 ft over so 20 squared + 20 squared = hypotnuse squared , so 400 + 400 = h suared , suare root or 800 =h ,or about 28 ft
With a 40 square, the sides are the square root of 40 = 6,32. Since we have a square the corners are 90 degrees. we have a right angle with two sides of 6,32. We can then find the diagonal of this right angle triangle by using Pythagoras. (6.32)^2 +(6.32)^2 equals the the square of the diagonal (80). And the square root of 80 is 8.94. And we only want half way across the diagonal so we divive by 2. =4,47.
What is interesting is you can skip the square root of 40 since you are going to be squaring it. So its 40 plus 40. 80. half the square root of 80. 4.47 feet.
Watch the video to get the correct answer. I could tell by inspection there is no way it's 4.47.
@@robertthomas5906 " there is no way it's 4.47."
Yes way. If the square contained 40 then the distance from corner to center is 4.47. If the EDGE measures 40 then the distance is 0.5 * sqrt( 40^2 + 40^2) Pythagorean Theorem]
@@thomasmaughan4798 You still did it wrong. Again, look at the video. He tells you. 40^2+40^2 is 1600+1600=3200. Sqrt of 3200 is 56.56. Half of that is.... not 4.47. It's 28.28. Which is why I said there is no way it's 4.47. That's because by inspection your 4.47, call it 5 would double to 10 and 10^2 is 100. Still way to short for the two sides. So it can't be 4.47.
Remember, you in the corner of the room. You want the distance to the center. I'm not sure what you're figuring out it's so wrong. I couldn't give you even partial credit.
@@robertthomas5906 "You still did it wrong"
THERE IS NO WRONG. There is only different and sometimes correct and incorrect. Right and wrong are moral judgments; correct and incorrect apply to methods.
These videos take advantage of (1) different readings of English combined with (2) a common human desire to label someone else as wrong (not just incorrect).
Thank you John. My world is a better place with your videos in it!
Understood at minute 11:00 with the formula you reminded me of which was stored in some corner of my memory. ;)
1600 (a square) +1600 (b square) = 3200
3200 = C square
Square root of 3200 = 56.26
The hypotenuse "C" is then 56.26 long.
Divided by 2 = 28.28
OK! I am ready to work on my geometry now. It's been a while. I was hesitant to get back into geometry but your video gave me confidence to refresh my knowledge about that part of mathematics.
And you reminded us the part about looking for a positive because we are talking about distance.
Even better with the short cut formula that was also sleeping in some corner of my brain.
Well explained Mr Math Man. :)
Multiply the length of the side by 1.414 to give you the length of the side opposite the right angle. i.e., 40 x 1.414 = 56.56. So you can multiply any number by 1.414 to give you the length of the side opposite the right angle.
I came up with 20 × sqrt of 2, or about 28.3 ft.
Love your videos but found it way easier to make a right triangle at the half way point of the square and figure out the length of the long side with (2) 20' sides.
And it's more elegant and precise to produce the exact answer (20√2) rather than cutting a real-number approximation in half!
I'd like to see anybody take this long to explain this problem. My goodness seemed forever.
The diagonal of a square is given by l√2. The distance to the center is half the diagonal. So (l√2)/2 => (40√2)/2 => 20√2 => 28.2842
My, oh my, that was REALLY mucking about in the mumbo jumbo. Why not just multiply the sine of 45 degrees by the hypotenuse? One step instead of three. You should be making videos on making math more complicated than it really is, just like John.
I used the same logic. In my head, I got ,"Something around 28 feet, plus a little bit." Good enough for me.
I would calculate it as 20'*sqrt(2). You can also use sqrt(a^2+b^2), where a and b are both 20 feet.
Pythagorus (maybe, according to recent news articles) says the square of the hypotenuse is equal to the sum of the squares of the other 2 sides. So:
40 squared plus 40 squared = 3200
Square root of 3200 divided by 2 = 28.28 (to 2 decimal places)
Ancient architects must have understood this, if not in a purely mathematical sense. I'm sure that the 3-4-5 building square must have been used. Even so, the proof is easy if done graphically/empirically. They must have understood squares, if not square roots. After all, they were just as intelligent as modern day humans. We often underestimate them. They probably just thought differently. I often wonder how the Romans designed buildings using Roman numerals. I've tried doing mathematics with them but failed miserably.
Simples !
I was a carpenter, so math was about 50% of my job. Here is a shorter more direct way. 40*1.414/2. 1.414 is the diagonal measurement of a 1" square. This came from my math book during my apprenticeship. This will only work on a perfect square.
Yep, exactly what I learned in apprenticeship school.
As long as it is a square, there is a very simple way of getting the answer. You just need to know that the square root of 2 is 1.414. From that value all you need is the 4.
Start by multiplying 40 x 4 then shift the decimal one place to the left. 40 x 4 = 160 --> 16.0 40+16=56 Now take the 56 and shift the decimal 2 more places to the left.
56 --> 0.56 Now add them together 56+0.56=56.56 Now you have the length of the hypotenuse but the question is how far to the center so half of 56.56 is 28.28 Enjoy!!
A really Simple way of figuring this out is, "What is the Square root of 800?"
Since the square consists four Equilateral right angle triangles, each with a hypotenuse of 40'. Using Pythagoras we know that the square of the Hypotenuse = the sum of the square of the other two sides, so 40 x 40 = 1600, half of 1600 = 800, Sqrt of 800=28.28
No such thing as an equilateral right triangle. No equilateral triangle is a right triangle, Grasshopper. If we use "equilateral" literally, all three sides would be of equal length, which is impossible in a right triangle. A square is an equilateral rectangle. Use the Law of Sines and you'll see what I mean.
Nice that you were allowed to edit but I weren’t…I meant isosceles triangle.
You Sir, make Mathematics come to life. THANK YOU
The first thing I did was to verify 40 foot square vs 40 square foot.
Second I know a 45-45-90 triangle the hypotenuse is 1.414 of the shorter sides.
Third short side is 40/2 = 20 feet * 1.414 = 28.28.
I got confused by 40' square. I questioned whether it meant 40' perimeter. Or 40 square feet. I figured the answer was either half of the square root of 200 or half of the square root of 40. I was always challenging the wording of problems.
The first step in this problem is getting the professor to clarify. Poorly worded problems like this and NOT clarifying are the difference between landing a rover on Mars and crashing a rover into Mars.
An isoceles right triangle (45,45,90) has sides of a,a,a*sqrt2. The right triangle formed with the hypotenuse from a corner to the center of a 40' square is a special triangle with sides of 20, 20 and 20*sqrt2, or 28 1/7.
¿Could you also just do sqrt(20^2+20^2) or 20 * sqrt(2), since you know half the distance of any side is 20 feet and it's 20 feet from the center of any wall to the middle, or because the sides are a nice even multiple of 10 you could do sqrt(2^2+2^2) * 10?
Yeah, I did it as 2x^2 = 1600, where the side of the room is the hypotenuse. Solving for x gives 20 * sqrt(2). It would have been cool if he showed both methods. It's a great way to demonstrate the beauty of math, how two different paths lead to the same destination. Like how you can derive the formula for the volume of a solid by doing different integrations.
My immediate approach: Center of one side(20), up to center of square(20). A2’d(400)+B2’d(400)= C2’d(800). Corner to center(hypotenuse) = sq root of 800, 28.28.
Here's another, slightly different, way to visualize it: If you draw two diagonal lines across the square, they meet in the center at 90 degrees. Now you have four right triangles, each on of which has the side of the square as the hypotenuse. The distance from the corner to the center is the length of the triangles' minor sides (which are all equal). The Pythagorean Theorem tells us that the length is the square root of one-half of the square of the hypotenuse. 40 x 40 = 1600; 1600/2 = 800; the square root of 800 is 20 radical 2.
Since it's a square, the two diagonals will, as well as intersecting at the centre, intersect at 90°. Thus, we have four isosceles, right-angle triangles, each with a 40' hypotenuse.
Let 20' equal 1 JOE (a random linear unit of measurement)
Therefore, each semi-diagonal is sqrt((2^2)÷2), or, sqrt 2. Which is 1.414 JOES
Thus the distance to the centre from the corner is 1.414 x 20' = 28.28'.
No calculator or pencil/paper required. But a knowledge of basic square roots is necessary.
Later---
I chose 2 for the length of the hypotenuse because I happened to know that sqrt2 is 1.414 without calculating or looking it up.
28' 3 7/16ths" (I think,,) (no calculator) I'm a carpenter, I square up foundation and house walls routinely. 3,4,5 triangle is the 'go to' solver on most jobsites.
You make something simple really complicated
When I was about 7 years old, Johnny Mercer and Danny Kaye taught me, "The square of the hypotenuse of a right triangle is equal to the sum of the squares of the two adjacent sides."
My methodology for solving this problem was a little different from yours, though. I bisected one of the right angles of the square, then bisected an adjacent right angle. This provided an isosceles triangle with two 45 degree angles (the two bisected 90 degree angles) leaving a right angle opposite the 40' hypotenuse of the created triangle. I know the two sides adjacent to the hypotenuse are equal, as their opposing angles are equal. Therefore, 2*x**2 (two x-squared) = 1600 (40 squared). X becomes the square root of 800, (using a calculator to compute the square root of 800) or approximately 28.28
what do you mean by a 40 ft square room? Are the sides 40 ft or is the area 40 square ft?
When a shape is described as "X Square" generally means that the shape is a square, with dimensions of "X" being both length and width. If he was talking area, he would have written it out as 40 square foot.
Square room 40 feet on a side. Two right triangles. a-1, b=1, c=1.414 (from memory).
Multiply 1.414 by 40, divide by 2 and one gets 28.28 feet.
28.28'
The hypotenuse of an isocelese right triangle with sides of 1 would be the square root of 2, or 1.414. then by similar triangles you multiply that times 20.
Calculator no es necessario.
I am just after the point of the video where you gave the answer, and my answer is correct. But I think i may have gotten the answer differently. Since it is a 40x40 room. I broke it up into 4 45° right triangles. Then using the calculator, I took 40 ÷√2 and got 28.28427124. Now this will only work on a square area. Now i will watch the rest of the video.
An angle will always be larger than side to side measuring. We quilters cut up fabric all the time and sew it back together. A half square triangle will be larger than half a square. A circle cut will also be larger, like a pizza, again an angle.
The time it took you to do this divided by 10 would be the correct amount of time to spend on it.
"A" squared plus "B" squared equals "C" square. A =40, B=40 thus 1600+1600=3200; C squared = 3200, c= 56.5685425. The center of room is half that so 28.2842712
28.28 feet. Since it is a square, there are right angles in the corners. the hypotenuse of two sides is 40 sq + 40 sq = Hypotenuse sq. the hypotenuse is the sq root of 3200, or 56.56 One half of that is the distance to the center.
If you draw a diagonal then you have a right triangle with two equal sides so the length of the diagonal is 40 times the square root of 2. To the center of the room is half this length so 20 times the square root of 2 or approximately 28.3 feet.
Love it, as soon as I saw the title I knew it about the square root of 2. Lol, one of my favorite things I learned carpenter’s apprenticeship school.
Find length of diagonal and divide by 2.
a squared + b squared =c squared.
Divide c by 2
~28.28'
Square is 40’ per side. A person at a corner will walk along the diagonal half way from one corner to the opposite diagonal corner. Using a right triangle to represent this approximately 28.3’
Thank you for the marh lessons.
A square room .. 40 x 40 .. and you want the distance from a corner to the centre.
To get the distance from one corner to the opposite one think of a right angle triangle.
The square of the distance from one corner to another = 40 squared + 40 squared
X squared = 1600 + 1600 = 3200
The distance from one corner to another is the square root of 3200
and then you want half of that, but I don't have a calulator on me to do the square root bit !!
A handy way is to consider the general properties of a square is to consider the simplest length of a side as unit length 1. Therefore the diagonal length, by Pythagoras’ theorem is the square root of (1 squared (=1) plus 1 squared (=1), i.e. (1+1 =2). So the diagonal of our simple square is the square root of 2. Tip: If there is one square root to remember it is the square root of 2; i.e. = 1.414 (quite a neat number isn’t it?). Now, a 40 foot square room (not 40 square-foot room) has each side 40 feet. Divide it in half because the centre of the room lies on a parallel line half way along the side (i.e. 20feet) and Multiply 20 by our general diagonal - the square root of 2 i.e. (2x1.414); therefore the centre of the room is 28.28 feet from the corner.
got it - 1/2 the diag. thanks.
Funny, I envisioned it as 40' being the hypotenuse, the length of the wall. The other two legs I envisioned as extending from each corner to the center. So my formula was 2Asquared = 40 squared. On further thought, I also saw it as A and B being 20', one half of the length of the wall with the hypotenuse running from the corner to the center of the room. Odd I never envisioned it as described in the video.
After reading the remarks, people need to understand the difference between a room that is 40 Sq. Ft., and 40 Ft. Sq.
So right. I also commented on two previous examples which gave an incorrect answer for the problem posed. You want a precise answer, then ask a precise question.
Or you people could finally go metric... 😮💨
28.28 feet
I took the square root of 2 (1.414) and multiplied it by 40, then I divided that answer by two in order to find center. Any years of being a machinist has taught me some shortcuts for math. 40 x 1.414/2 = 28.28
My method was totally different, same answer. Not sure even how you arrived at that. I just used a triangle of 20 x 20. Not even like the example demonstrated.
Approximately 36 given that that the hypotenuse of a 45deg triangle is approximately 1.4 the sides 1/ root2 then half would be the distance to centre
Depends on the dimensions.
So glad I don't need to know this information for anything in my life.
half the room diagonal triangle from centre to another corner you still have 45, 45, 90 triangle, but now hypotenuse is 40. sin and cos 45 deg is 0.707, 0.707x 40 = 28.28
Easier to go 20’ down one side from the corner and then from that point perpendicular to the side then front thatpoint 20’ to the center. You now have a right triangle with 2 equal length sides. With these triangles the hypotenuse is equal to the square root of 2 times the length of a side. Which I’m sure you know. Like the videos, I’m what you call old school. Graduated HS in 64 and college in engineering In 69.
The mathematical calculation comes out to the square root of 800. However, that assumes you are standing right on the corner of the room, which is impossible. I'm not a ghost nor can I phase through matter. So, since my feet are 11 inches long and ther will be 2 inches between my heel and the actual corner, the the distance to the center of the room is sqrt(800)-11"-2"
28.28'-11"-2"
(28.28×12)-13
339.42"-13"
321.42" or 27.2'
The diagonal of 1ft x 1ft = 17ins so diagonal of 40 ft is 40 x 17= 680ins , center= 680÷2 = 340 ins or 28 ft 4 ins .
You are great John.I really enjoy watching your videos.
I wanted half so a right triangle 20^2 + 20^2 = sqrt(800) = 28.28
I read the question as a 40 square feet room (as opposed to your square room with 40’ sides)which threw me off. I couldn’t figure out the sides: 5’ x 8’ for example? This is why I failed math in high school I guess. I never read the questions correctly, lol 😂
Or. You could just multiply the side by .7 because your shop teacher/math teacher had you memorize that the diagonal of a square is 1.4 x the side. A sailor would also know that 1.4 times the distance up wind is the minimum amount you will have to sail to reach the weather mark.
On the bright side, I knew to go to A^2 + B^2 = C^2, 40^2 = 1600, 1600* 2 = 3200. I just didn't know square root of 3200 in my head, closest I got was just under 60 feet. Half of that would mean just under 30 feet.
Way easier to first cut the sides in half to 20 ft. Then, using the 45 deg rt triangle rule, it is just 20*1.414 = 28.28.
14 ft. square root of 200
20x20 room
10 ft along one side and 10 ft to center
hypotenuse
28.28 ft!
Can you cut it short please?
On a 1 : 1 rt triangle the hyp. = 1.414 ratio = square root of 2
I found something new how to measure any distance with a square. all you needs is a sight on the right side and on the left side a sight on a slide bar on the left side and a tape measure a crossed the top. With a 10 foot square you could easily measure the distance to the moon or sun in feet. I would like to discus this with table class math. I think this is how they did it thousands of years ago before Algebra or trig.
A (40ft) squared plus B (40ft) squared = C squared. 40x40 = 1600 + 1600 = 3200 The square root of which is 56.56 divided by two (half the distance from corner to corner) = 28.28 (your answer)
Is the 4O feet 10 * 4 40*4 1 side or all 4
I would use Pythagorean theorem.
I love the problems that the 3,4,5 rule jump out of easy to do with out a calculator. This isn’t one of those.
Author didn't use a precise description of the area in question in the header:
But assuming a 40 square foot square room;
each side = 6.32 sq ft . In a corner, you'd be looking at a diagonal to the center. Using Pythagoras, diagonal works out to 8.93, center would be half the length of the diagonal or about 4.46 away from the corner.
Of course the author assumed a square of 40 linear feet on each side. Answer is about 28.28.
It's a 40x40 foot square room, which is a 1600 square foot room. A 40 foot square room would be 6.324+ a side, which is the square root of 40.
I remember this from construction jobs when laying out building lines. A squared plus B squared equals C squared(the diagonal) then I took half of C to get the answer.
I got the right answer "20 x sqrt(2)", but I think the question is poorly phrased.
No, it's not poorly phrased. It just requires analytical skills to interpret correctly.
I got roughly 29' but that was in my head and without a calculator, which would have given an accurate answer.
so to got (40) either way and 2 right triangle with at 45 degrees so sin or cosine it edit pythagorus
This is the latest of your poorly worded problems. Is a “40’ square room” a room with an area of 40 square feet, or a square of 40 foot sides?
28.28 ft
A 40' square room is either a room that has an area of 40 square feet, meaning that each of its sides are much shorter than 40 feet, given that they're a square root of 40, or the room is 40 square feet, but then it's no longer a square room. You've raised a contradiction and then changed the actual terms of the question by using 40 feet as the room's length and width, which then renders the room to be much larger than just 40 square feet. Which is it then?
I took it to be a forty foot square (i.e., a "room of forty square feet"). Reading comprehension (or lack thereof) strikes again, so of course I got the wrong answer. I used to do this all the time on math tests; use the proper procedure but misinterpret the instructions.
I reread the problem as he states in oh so many videos, a 40 ft square room is very, very different than a 40 square foot room. People are adding in words that are not in the problem. First read through, I did the same thing of thinking 40 sq ft, but that didn't make sense as NO room dimensions were given, thus the reread.
Yeah, I noticed the lack of dimensions and the distance from corner to center differs greatly if its 2 * sqrt(10) by 2 * sqrt(10), versus 1 ft by 40 ft.
I had to do a double take on the wording as well. If this were a test question, some of the students would answer this differently because of interpretation. The unfortunate problem is that these students would be punished (with their grade) even if their mathematical methodology was spot on. Yes, interpretation is very important, but wording ambiguity can nullify the effect of an otherwise good math question.
I do believe that the question could be worded in a way that is far more clear. Example: You have a square room with a side that is 40 feet long, what is the measurement from the center of the room to one of the corners?
@@MathematicPlumber Just because wording requires analytical interpretation to understand correctly does not mean it is ambiguous.
Wording it as "a square room with 40 foot sides" breeds lazy thinking.
Didn't watch the video. I don't know why it takes 22mins to explain this. Old mate Pythagoras is probably the only thing I remember from my school days nearly half a century ago. "Square of the hypoteneuse is equal to the sum of the squares of the other two sides." 40x40=1600. 1600 +1600=3200. √3200=56.56 (rounded). Centre is halfway along, so 28.28ft. Then i just skipped to the end to see if you got it right. Now, back to watching cat videos.
I solved this in my head in less than a minute, because I know that a 1 x 1 square has a diagonal of the square root of two, by Pythagorean. So its just a 20x20 square to reach from the corner to the middle, so 20 times the square root of 2.
That's a bit confusing, semantically at least, for non-natives. I've read it as 40 square feet room, not a square 40'×40'. 😊
Bad worded question is right!! I read it as 40' room that is square.(40x40 & 56.57 hypotenuse (28.285 to the center)) instead of, like it says a room with 40 ft² ie . 4x10, 2x20, 5x8...etc.(5.39,3.32,4.72 to the center)
BTW. A square room that's 40ft ² has measurements of 6'4" X 6'4" and is 5'4⅔" from corner to center.😊
(P.S. I have a 40 sqft guest bathroom and the toilet is in the shower stall )
Well, I assumed it wasn't 40 Sq ft, but that left me with the problem of deciding whether each side was 40 ft, or the sum of sides were 40 ft - as both could be described as a 40 ft square room. Also left unknown was the height of said room. One assumes it's Flatland, as the room is a square, not a cube - but in Flatland it's a line, not a square. Are you sure we're in a room? Can't the room be omitted as unrelated data? Sigh - it's too early for such issues. I'll say it's 8 steps and let you calculate my height 😊
I think that if it was an area, it would have been worded 20 square ft room as opposed to a 20 ft square room.
1-1-root of 2 rule
20(root of2)
I know that the ratio of half the hypotenuse to a squares side is SQRT (.5).
So, I just multiply 40 times SQRT (.5) and I get SQRT (800)
Judging solely by the question that's initially displayed (i.e. haven't watched the video), I would need some clarification due to the way it's worded. Does it mean it's a square room that's 40 ft on each side or does it mean that it's a 40 sq ft room?
So, I read this as a 40 sq feet room. As the area of the room was 40 square feet. 😅 I had to start watching the video to get a grip on it, and then I realized it is a 40 feet on a side. Sometimes I share this videos with my 14 years old grandson. But, I think I will share daily . 😊
The room is 40ft square as stated, not 40 square feet. The answer therefore is 56.67 ft.
So did I. It clearly says 40 square feet.
You have a trisngle with 45deg in my head I knew it would be half way 40/2=20 times the Tangent of 45deg=sqrt(2)=1.4.14 = 28.28 aprox
When I hear 40 foot square room, I'm thinking a room that has 40 square feet, which means each wall would be about 6. 32 feet in length. which would make it about 4.46 feet to the center of the room, from a corner. or 53.5 inches. LOL (a small walkin closet. LOL)
John -- your math question wording is not as precise as we've come to expect.
I first assumed it was a room 40 ft² (assumed a square) which meant, corner to center is 2•√10 or about 6.324 feet or just under 6ft 4 inches. With the size of the human body, you're about 5 feet away (assuming it's square).
But if the room is a square room 40 feet per side then center to corner is √800 or 20√2. That comes out to 28.284 feet or just over 28 ft three inches. With the average size of the human body your face is about 27 feet away.
"You are in a square room with sides 40 feet each. You want to install a bar (string/clothes line/something straight) from the corner to the center. How long will the bar (or whatever) have to be?"
X by 1.414 divide by 2 = 28.28
In my mind I see....
A square
Then a right triangle
Then 1/2 a hypotenus
Then a smaller right triangle
Then the length of the shortest side 🤔
just a note to the teacher: 'a 40 feet squeare room' means the area of the room is 40 feet .. maby be clearer in the future... assuming one side is 40 feet .. the math ppl presented r okay...
(and as this isent advance math other options are omitted)
I did a similar solution, but got a different answer. As I misunderstood, I thought the area of the room is 40 square ft. 😖😣😫
It's easy to do, all too often people incorrectly say feet squared when they mean square feet. I had to presume a math instructor would use the correct terminology.
Excellent. I'd forgotten about the sqrt of 2. Used it in plumbing to get the size of a copper tube running at 45 degrees to the next. 1.414. Guy working with me said, "What the hell you doing?" I looked like Einstein. So funny. All great videos.
to the exact center ? would it be 28 ft 3 7/16 inch.
40 times the square root of 2 divided by 2 equals 28.28. Takes thirty seconds.