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Hmm. I did it this way; 5m goes into 16m squared, 3.2 times. 5m x 3.2m is 16m squared. Solved. 3.2m + 4m is 7.2m. 7.2m goes into 36m squared 5 times. Solved for X = 5m.
I was so pleased I could solve this! 😂 the past few were a different level but mind expanding I did the first method but the second method is super obvious once you showed it!
If you calculate in decimals then it is the quickest way provided that you are fast in mental maths. Took me about 4 secs to find x by using decimals. Compared to extra seconds needed to realize the importance of completing the big rectangle with the missing corner one having 4 & 5 as sides. So the intuitive approach took about 6 secs. Decimals went like 16/5=3.2 ➡ 4+3.2 = 7.2 ➡ 36/7.2 ➡ 5
@Meelenko In India, calculators aren't allowed in schools. So we had to find shortcuts & memorize the multiplication tables as much as possible. About 4 decades back in high school, I memorized till 100 like others. Now, I have lost a part of it, thanks to using calculators & being out of practice 😀
@@MrSudeepdas I have a mathematician friend (40 year old) - and to my surprise, he also immediately calculated both 16/5= 3.2, and 36/7.2 = 5. He almost saw no point in solving such triviality :-) But for my simpleton brain dividing decimal numbers is very, very foggy, while I immediately imagined 'invisible' 4x5 = 20m2 rectangle up right, which meant both "sides" were 36m2, and have equal base length.
@@Meelenko Simple decimals that are not irrationals are easier to use than fractions. Basically by the time I finished reading this problem the answer was there in front of my eyes. Most probably the same happened with your friend as well. Its quicker than pressing buttons on the calculator.
The second method is faster only because it is a special case, if the areas of the 2 rectangles were different, additional steps would have been necessary. I think the first method is more standard
Hello Susanne, I think I've found the secret of your success: You deliberately don't choose the simplest of explanations. That forces people to think and obviously to know better. And therefore also to comment. Clever. You can join in. It's fun. Thank you and best regards.
Brilliant video. I am trying to help my 15 year old son with his maths - and this kind of video is excellent - very clear explanations and a nice pace at which to work. Thanks and keep up the good work!
Solution: The height of the smaller rectangle is 16/5 m, because a * b = A, with a = 5 and A = 16. The height of the bigger rectangle therefore is 4m + 16/5 m. Using the same a * b = A equation, we get: x * (4 + 16/5) = 36 x * (20/5 * 16/5) = 36 x * 36/5 = 36 |*5/36 x = 5 Alternatively, we can use the "missing" rectangle at the top right, that is 4m * 5m = 20m² and add it to the smaller rectangle to get a total area of 36m², which is the same as the left rectangle and therefore has to be the same width.
Did this in my head in under a minute looking at the thumbnail - calculated that the length of the 16sqm rectangle's other side was 3.2m (16/5) which made the long side of the other rectangle 7.2 and, knowing that 5x7=35 and 5x0.2 =1, it was 36/7.2 = 5. So, similar to the long method but without that faffing about with fractions (which, BTW, was solved the second it's apparent that the long side is 36/5, since the numerator was equal to the area of the rectangle, and if 36/5 gives you the length of the long side, the long side multiplied by 5 would give 36sqm and therefore x=5) Method 2 is only fast in cases like this, where the sum of the area of the two small rectangles equals the area of the large rectangle. If the area of the tall rectangle had been 30sqm instead of 36, you'd need to do some extra calculations to derive x.
Some people may not know that you can work backwards from an area formula to find a side. If you are using area of a rectangle = base*height, or area of a triangle = base*height/2, you can substitute in any two of area, base, or height to find the third one. I made a video at ua-cam.com/video/OXHpj03_FN4/v-deo.html where I showed five ways of finding the side of a triangle, and I think the simplest way was using the area formula to find a side. In math, a formula or procedure could be taught as useful one way, but also be useful in other ways.
Sorry, I just did 36/7,2 in my head. The complete solution took me about a second. It took me way longer to check if I was correct. Both your explanations were incomprehensible to me. It brought back all the memories why I left school and went out to sea to become a ships engineer.
that is scary! You are a ship's engineer and find this problem difficult. Please tell me the names of the ships you engineer so i can make sure to stay off of them.
Місяць тому
I did it a bit differently. I found the area of the big rectangle minus the small rectangle (36 m^2 - 16 m^2). The remaining rectangle has an area of 20 m^2 with height of 4m and width of x. Thus, x = 20 m^2 / 4m = 5m. Nice little exercise.
How do you know that the left rectangle minus the right one leave a whole rectangle? That only works if the left rectangle is the same width as the right one which you don't know initially...
Місяць тому+1
@@ChrisVenus Hmmm... good point. I was just lucky then and stumble upon the solution by accident.
I'd say your solution isn't actually far off of the solution 2 in the video mathematically. That kind of only works because completing the rectangle happens to make two equal sized areas and that only happens when x = 5.
I started with the small rectangle. Area is 16 sq m so height is 16/5 =3.2. Adding the 4m gives the height if the large rectangle = 7.2 m. So x is 36 sq m / 7.2 =5 metres. Which was what was wanted.
Lösung: Höhe des rechten Rechtecks = 16/5 = 3,2, Höhe des linken Rechtecks = 3,2+4 = 7,2, x = 36/7,2 = 5[m] Solution: Height of the right rectangle = 16/5 = 3.2, Height of the left rectangle = 3.2+4 = 7.2, x = 36/7.2 = 5[m]
Giving that the picture uses correct dimensions just do 4x5 and then even an idiot can see that x must be 5 straight away. Since 4×5+16=36 However you solve this, this is elementary school level math and problem solving at best. So I conclude you're doing this to farm more comments. Good job, you got me.
Mostly, teachers and mathematicians prefer you to work out the answer using formulations of equations and performing the right mathematical process to arrive to an answer. Sure you got the right answer, but can you show how you got to that answer?
hey, glad to have found your channel! it's like as if, "mind your decisions" finally got a face 😅 also, awesome accent! (you're doing pretty well! you fail to convince yourself to stick your tongue between your teeth [so, just like every other German ever, lol] but retract your tongue when you say your 'r's for an impressive sense of rhoticity, which is almost unmatched by most of your countrymen. just the melody is lacking, which is a bit of a surprise for a girl since they can usually sing pretty well and are therefore better in imitating foreign intonations.)
fractions drive me nuts sometimes... I simply did 16/5 t get the length of the rest of the line that =4m... which is 3.2 ... 36/3.2 = 5 simple use of surface area of a rectangle rule. I'm more of a visual mathematician. like this example I know what numbers to feed the calculator and can really get to specific answers or sometimes even just apporixmates if that is al the detail that is required... my teenage daughter is a math wiz though , She is almost in highschool and still scores 100% in math on test after test...
Hallo Susanne, ich glaube, ich habe das Geheimnis deines Erfolges gefunden: Du wählst bewusst nicht die einfachste aller Erklärungen. Das zwingt die Leute zum Nachdenken und offensichtlich auch zum Besserwissen. Und damit auch zum Kommentieren. Clever. Man kann mitmachen. Macht Spaß. Danke und liebe Grüße.
why did you make somthing simple to get complicated? You diluted the solution that is straightforward, as many people said in the comments. It took me five seconds to solve this ( I'm a bit slow, I know)
Hello- really enjoy your videos- but I watch them on a smart TV and it’s not easy to click the thumbs- please could you make the end of the videos longer to give me chance- I imagine that if I have this issue - others must- I’d hate you to missing out on likes !
Hey math friends! If you’re enjoying this video, could you double-check that you’ve liked it and subscribed to the channel? It’s a simple equation: your support + my passion = more great content! Thanks for helping me keep this going - you’re the best!
I didn't see the second method af first, nicely done! I thought you will substract 16 from 36 and then calculate X
Hmm. I did it this way; 5m goes into 16m squared, 3.2 times. 5m x 3.2m is 16m squared. Solved. 3.2m + 4m is 7.2m. 7.2m goes into 36m squared 5 times. Solved for X = 5m.
Yep, that's how I did it
x=36/7.2=360/72=40/8=5 unit
@@garyr1639 ditto
that's very much so the first method she showed
@@HxTurtleexcept for the part where she made it more complicated….. this is definitely a simple way to explain it.
It’s crazy that I found your German channel first. I’ve been using it to help me learn German since my son decided to study it.
I solved it the first way and was really pleased with myself. Then you showed the second and I couldn't believe I didn't think of that! 🤪
Love the second method, didn't think of it. I'm going to keep watching you until I'm too smart for my own good. :)
Composite shapes is a classic mathematics problem. The second method is great for helping students identify relationships between quantities .
I was so pleased I could solve this! 😂 the past few were a different level but mind expanding
I did the first method but the second method is super obvious once you showed it!
If you calculate in decimals then it is the quickest way provided that you are fast in mental maths.
Took me about 4 secs to find x by using decimals.
Compared to extra seconds needed to realize the importance of completing the big rectangle with the missing corner one having 4 & 5 as sides. So the intuitive approach took about 6 secs.
Decimals went like 16/5=3.2 ➡ 4+3.2 = 7.2 ➡ 36/7.2 ➡ 5
I find calculating 36/7.2 in seconds incredible. Unbelievable, even 😛
@Meelenko In India, calculators aren't allowed in schools. So we had to find shortcuts & memorize the multiplication tables as much as possible. About 4 decades back in high school, I memorized till 100 like others. Now, I have lost a part of it, thanks to using calculators & being out of practice 😀
@@MrSudeepdas I have a mathematician friend (40 year old) - and to my surprise, he also immediately calculated both 16/5= 3.2, and 36/7.2 = 5. He almost saw no point in solving such triviality :-) But for my simpleton brain dividing decimal numbers is very, very foggy, while I immediately imagined 'invisible' 4x5 = 20m2 rectangle up right, which meant both "sides" were 36m2, and have equal base length.
@@Meelenko Simple decimals that are not irrationals are easier to use than fractions. Basically by the time I finished reading this problem the answer was there in front of my eyes. Most probably the same happened with your friend as well. Its quicker than pressing buttons on the calculator.
The second method is faster only because it is a special case, if the areas of the 2 rectangles were different, additional steps would have been necessary. I think the first method is more standard
Great lesson! Thank you Oh Queen...
Ha! Solved this! 🤣 Love this channel! Thank you 💛💛💛
This was the first one i did fully on my own and got correct! Thanks!!
Such a beautiful explanation! Thank you!
Hello Susanne,
I think I've found the secret of your success: You deliberately don't choose the simplest of explanations. That forces people to think and obviously to know better. And therefore also to comment. Clever. You can join in. It's fun. Thank you and best regards.
wish that I had had you as a math teacher ( 60 plus years ago !!!! )
I did the first method in my head, but i like your second method much better 😊
Excellent explanation, really enjoyable. Well done
using the second method was so easy I was sure I had made a mistake. 😄
Wonderful the second solution
Love you
I really appreciate the graphical nature of the problem/solution!
🙂
Brilliant video. I am trying to help my 15 year old son with his maths - and this kind of video is excellent - very clear explanations and a nice pace at which to work. Thanks and keep up the good work!
Best explanation coming with best smile! For sure we subscribe!
Solution:
The height of the smaller rectangle is 16/5 m, because a * b = A, with a = 5 and A = 16.
The height of the bigger rectangle therefore is 4m + 16/5 m.
Using the same a * b = A equation, we get:
x * (4 + 16/5) = 36
x * (20/5 * 16/5) = 36
x * 36/5 = 36 |*5/36
x = 5
Alternatively, we can use the "missing" rectangle at the top right, that is 4m * 5m = 20m² and add it to the smaller rectangle to get a total area of 36m², which is the same as the left rectangle and therefore has to be the same width.
The second one is fantastic easy and fast
I only do these math exercises to see and hear Susanne 🤣
Thanks for a great lesson. 👏👏👏👏🙏🏿
Good morning! I guess what solution you use depends on if you prefer equations or visuals. Again, thanks for the refresher!
Loved the lateral thinking to get the quick method - I was happy I got it the first way but sad I missed the quick one
I solved it the first way, bu I love the simplicity of the second solution.
Did this in my head in under a minute looking at the thumbnail - calculated that the length of the 16sqm rectangle's other side was 3.2m (16/5) which made the long side of the other rectangle 7.2 and, knowing that 5x7=35 and 5x0.2 =1, it was 36/7.2 = 5.
So, similar to the long method but without that faffing about with fractions (which, BTW, was solved the second it's apparent that the long side is 36/5, since the numerator was equal to the area of the rectangle, and if 36/5 gives you the length of the long side, the long side multiplied by 5 would give 36sqm and therefore x=5)
Method 2 is only fast in cases like this, where the sum of the area of the two small rectangles equals the area of the large rectangle. If the area of the tall rectangle had been 30sqm instead of 36, you'd need to do some extra calculations to derive x.
I delved into the world of decimals, it seemed much simpler that way.
From the title I thought it was "find the length (number of digits) in x factorial", which is a fascinating question that I might tackle later today
This is a fun problem to solve.
Math is beautiful!
Some people may not know that you can work backwards from an area formula to find a side. If you are using area of a rectangle = base*height, or area of a triangle = base*height/2, you can substitute in any two of area, base, or height to find the third one. I made a video at ua-cam.com/video/OXHpj03_FN4/v-deo.html where I showed five ways of finding the side of a triangle, and I think the simplest way was using the area formula to find a side. In math, a formula or procedure could be taught as useful one way, but also be useful in other ways.
Dankeschön ❤❤
16=5*z; z=16/5; y=z+4=16/5+4=(16+20)/5=36/5; 36=x*y, x=36/y=36/(36/5)=5
Sorry, I just did 36/7,2 in my head. The complete solution took me about a second. It took me way longer to check if I was correct.
Both your explanations were incomprehensible to me. It brought back all the memories why I left school and went out to sea to become a ships engineer.
that is scary! You are a ship's engineer and find this problem difficult. Please tell me the names of the ships you engineer so i can make sure to stay off of them.
I did it a bit differently. I found the area of the big rectangle minus the small rectangle (36 m^2 - 16 m^2). The remaining rectangle has an area of 20 m^2 with height of 4m and width of x. Thus, x = 20 m^2 / 4m = 5m.
Nice little exercise.
How do you know that the left rectangle minus the right one leave a whole rectangle? That only works if the left rectangle is the same width as the right one which you don't know initially...
@@ChrisVenus Hmmm... good point. I was just lucky then and stumble upon the solution by accident.
I'd say your solution isn't actually far off of the solution 2 in the video mathematically. That kind of only works because completing the rectangle happens to make two equal sized areas and that only happens when x = 5.
Susanne gesellt sich zu Andy Math, dem ich auch schon lange folge. How exciting!! 😊😊
I started with the small rectangle. Area is 16 sq m so height is 16/5 =3.2. Adding the 4m gives the height if the large rectangle = 7.2 m. So x is 36 sq m / 7.2 =5 metres. Which was what was wanted.
You just need to complete the rectangle that is 4x5. And you have on the right 20+16=36 like on the left. Because 36=36, X=5.
I considered the second method after I solved problem using the first method. Good news for me is I actually solved both ways this time! Ray
I would have done the fast way first, but then second guessed myself. I would have then gone to the long way to confirm!
That's one I could do!
good presentation
brilliant!
Lösung:
Höhe des rechten Rechtecks = 16/5 = 3,2,
Höhe des linken Rechtecks = 3,2+4 = 7,2,
x = 36/7,2 = 5[m]
Solution:
Height of the right rectangle = 16/5 = 3.2,
Height of the left rectangle = 3.2+4 = 7.2,
x = 36/7.2 = 5[m]
Great work my fellow Mathematician content creator ❤❤❤ added my subscription support
Giving that the picture uses correct dimensions just do 4x5 and then even an idiot can see that x must be 5 straight away.
Since 4×5+16=36
However you solve this, this is elementary school level math and problem solving at best. So I conclude you're doing this to farm more comments. Good job, you got me.
Mostly, teachers and mathematicians prefer you to work out the answer using formulations of equations and performing the right mathematical process to arrive to an answer. Sure you got the right answer, but can you show how you got to that answer?
Make a square above the smaller one of 4 x 5 = 20 m^2. 16+20 = 36 M^2, -> equal areas with same longer side, therefore x = 5.
That’s what I did in my head. And I don’t know math.
hey, glad to have found your channel! it's like as if, "mind your decisions" finally got a face 😅
also, awesome accent! (you're doing pretty well! you fail to convince yourself to stick your tongue between your teeth [so, just like every other German ever, lol] but retract your tongue when you say your 'r's for an impressive sense of rhoticity, which is almost unmatched by most of your countrymen. just the melody is lacking, which is a bit of a surprise for a girl since they can usually sing pretty well and are therefore better in imitating foreign intonations.)
Beautiful lady , with a beautiful mind 😊
Ja to policzyłem w 15 sekund 🙂
5 . y = 16 m²
y = 16 / 5
y = 3,2 m
(4+y) . x = 36 m²
x = 36 / 7,2
x = 5 m
Convert 4 to 20/5 and find that 20/5 + 16/5 = 36/5
36/5 * 5 = 36
x = 5
@@willzhao5889 clever! Thanks.
I did it using the first method but used the decimal values over fractions.
1 minute for solution (I stopped at 0:17): 16/5 = 3.2-->4+3.2=7.2-->36/7.2=5, X=5.
I think its faster then second solution. 🤪
Just draw a line across at the height y, so the upper part of the first rectangle is 4x = 20. Wow, x=5. Shocking methods used here.
Easy one! x = 36/(4+(16/5)) = 5m
36/(4+16/5) unit
That's how I did it too.
Same... better at algebra then geometry.
x = 5. Did it in my head - about 10 sec.
x(4+y) = 36
5y = 16
x (4 + 16/5) = 36
x = 36•5/(20 + 16)
x = 5
16/5=3,2. 36/4+16/5=7,2.36/7,2=5
Going from the video title, x! = 120
😂
Nice!
I actually did with 1st method 😁
That was also the first method that came to my mind 😀
16 / 5 = 3.2
3.2 + 4 = 7.2
36 / 7.2 = 5
Therefore x = 5
Method 2 is what I did
36 cm^2 = x(16 ÷ 5 + 4) cm = x(7.2 cm)
x = 36 cm/(7.2) = 360 cm/72 = 45 cm/9 = 5 cm
fractions drive me nuts sometimes... I simply did 16/5 t get the length of the rest of the line that =4m... which is 3.2 ... 36/3.2 = 5 simple use of surface area of a rectangle rule.
I'm more of a visual mathematician. like this example I know what numbers to feed the calculator and can really get to specific answers or sometimes even just apporixmates if that is al the detail that is required... my teenage daughter is a math wiz though , She is almost in highschool and still scores 100% in math on test after test...
16/5=3.2 4+3.2=7.2 36/7.2=5
If Pricess Leia went to University instead of leading the rebellion against the empire ❤
Fun tastic
Why not subtract 16 from 36 leaving 20m2 and use the 4m side 20 / 4 =5 m
It took me just a sec to answer it.. that question is too easy for an Asian like me😂
Or
16/5=3.2.
36/7.2=5.
4.932
36-16=20/4=5
5!=120
Using my mental faculties, an inner voice told me that 5. :) :) :)
Length of x! is 120
Factorial
Solved this in 45 secs in my head with the assist of a calculator. Could have used pencil and paper
Isn't it easiest to divide 16 by five getting y=3.2, add 4 to 3.2= 7.2, divide 36 by 7.2=5? Although I get that what you showed is more educational~
Hallo Susanne,
ich glaube, ich habe das Geheimnis deines Erfolges gefunden: Du wählst bewusst nicht die einfachste aller Erklärungen. Das zwingt die Leute zum Nachdenken und offensichtlich auch zum Besserwissen. Und damit auch zum Kommentieren. Clever. Man kann mitmachen. Macht Spaß. Danke und liebe Grüße.
I use the first metod. The second is realy much easier. But it is mor difficult do see.
Sorry for not orthodox math... but I jus came that the small box is 3.2x5, then the rest easy.. 4+3.2 (5)
х=5, решил через 10сек ver very easy
Awesome, that you solved it so quickly!
16÷5=3.2+4=7.2)(36.7.2=5
(36 m^2)/ [(16/5 + 4)m] = 5 m
36÷7.2=5
Its so easy everything is given there answer is 5
It is fastwer but It is a guess. You Can not know they are the same
why did you make somthing simple to get complicated? You diluted the solution that is straightforward, as many people said in the comments. It took me five seconds to solve this ( I'm a bit slow, I know)
3 basic operations and you find the x to be 5.
5! = 120
x=5 . [ 36/((16/5) +4)]
16÷5=3.2+4=7.2)(36÷7.2=5
5
16÷5=3.2
3.2+4=7.2
36÷7.2= 5
X=5
Worked this out in my head in 2 minutes
5 in three seconds.
Hello- really enjoy your videos- but I watch them on a smart TV and it’s not easy to click the thumbs- please could you make the end of the videos longer to give me chance- I imagine that if I have this issue - others must- I’d hate you to missing out on likes !