Thank you so much Robinson for your continued love and support. Many many thanks for taking the time to leave this comment. Take care dear and stay blessed😃 You are awesome. Keep smiling😊
I didn't need any help solving this problem as it was one of your easiest. I just want to add that your explanations are so thorough that it is always easy to follow along as you demonstrate the solution.
The triangle “PQR” is a 30-60-90 triangle. All 30-60-90 triangles have the hypotenuse equal to twice the short leg and the long leg is always equal to (“sq. root of 3” x the short leg)
The heiht of the triangle can also be found using Herons formula for an equilateral triangle - the sides are of length 2 nad the h=sqr3/2 *s where s = 2 => height h = sqr(3) :)
Got it but was unsuccessful trying to work it without using the glaring triangle in the middle. Used the height in the middle triangle + 1 + 1 and got the length of the side easily. Excellent brain-teaser, let's roll PreMath.
@preMath thanks, for your great posts. but we can solve this problem easier. since the SPR triangle is an equilateral triangle, so each angle is equal to 60 degrees, so the QP line is equal to 2*r*sin(60), so the rectangle has one diameter equal to 4 and another one equal to 3.732. and then the problem is solved.
Answer 8+ 4 sqrt 3 or 14.92 7:36 the equilateral triangle formed height is 2^2 - 1^2 = n^2 4-1 = n^2 sqrt 3 = n the remaining length of the smaller side of the rectangle is 2 (1+1) So the length of the smaller side of the rectangle is 2 + sqrt 3 the length of the larger side of the rectangle is 4 (since the diameter of each circle is 2 and there are two circles). Area then is 7:36 4 (2+ sqrt 3) = 8 + 4 sqrt 3 or 14.92
Join the centres of all circles to form a triangle. Half of that triangle is a right angle triangle whose base is 1 and slant side is 2, so the height is sqrt 3, So the height of the rectangle is 1+sqrt3+1 = 3.73. So are of Rectangle = 4x3.73 = 14.92
A simpler method: The three circles touch at a 60 degree point on each. Sin(60)=0.866. Add 1 for the radius, multiply by 2 for the lower circle: 2(0.866+1)=3.732 for the height. 3.732 X 4 = 14.928.
Thanks Alexandre for the feedback. I thought about talking about equilateral triangle as well when I was making the video. You are awesome 👍 Take care dear and stay blessed😃
I agree that's how I approach it, and of sides 2, 2, 2 hence height is sqrt 3, so the width of the rectangle is sqrt 3 +1 +1 or sqrt 3 + 2 and the length is 4.
Thanks Shiva dear for such an elegant feedback. Thank you so much for taking the time to leave this comment. You are awesome 👍 Take care dear and stay blessed😃
Very nice explanation....I am sure students will fall in love with your style of teaching.....Kudos to your efforts!!!
Thank you so much Robinson for your continued love and support. Many many thanks for taking the time to leave this comment. Take care dear and stay blessed😃 You are awesome. Keep smiling😊
I didn't need any help solving this problem as it was one of your easiest. I just want to add that your explanations are so thorough that it is always easy to follow along as you demonstrate the solution.
Knowing the way you work I got this in less than a minute using just mental arithmetic :-)
The triangle “PQR” is a 30-60-90 triangle.
All 30-60-90 triangles have the hypotenuse equal to twice the short leg and the long leg is always equal to (“sq. root of 3” x the short leg)
Thanks again Pythagoras. Solved it. I feel like a genius.
The heiht of the triangle can also be found using Herons formula for an equilateral triangle - the sides are of length 2 nad the h=sqr3/2 *s where s = 2 => height h = sqr(3) :)
Or 4x (1+2xSIN(60 degrees)+1) using trigonometry.
Got it but was unsuccessful trying to work it without using the glaring triangle in the middle. Used the height in the middle triangle + 1 + 1 and got the length of the side easily. Excellent brain-teaser, let's roll PreMath.
Finally an easy one.
S=4(2+√3)≈14,93
@preMath
thanks, for your great posts. but we can solve this problem easier. since the SPR triangle is an equilateral triangle, so each angle is equal to 60 degrees, so the QP line is equal to 2*r*sin(60), so the rectangle has one diameter equal to 4 and another one equal to 3.732. and then the problem is solved.
Extremely beautiful calculation
Thank you so much, this was so helpful ❤️
V nicely explained .Thank you.
4 × (2 + square root of 3)
Not difficult one.
Tks, have a good time~
Answer 8+ 4 sqrt 3 or 14.92 7:36
the equilateral triangle formed height is 2^2 - 1^2 = n^2
4-1 = n^2
sqrt 3 = n
the remaining length of the smaller side of the rectangle is 2 (1+1)
So the length of the smaller side of the rectangle is 2 + sqrt 3
the length of the larger side of the rectangle is 4 (since the diameter of each circle
is 2 and there are two circles).
Area then is 7:36 4 (2+ sqrt 3) = 8 + 4 sqrt 3 or 14.92
Join the centres of all circles to form a triangle. Half of that triangle is a right angle triangle whose base is 1 and slant side is 2, so the height is sqrt 3, So the height of the rectangle is 1+sqrt3+1 = 3.73. So are of Rectangle = 4x3.73 = 14.92
Length = 4. Height = 1 + 1 + ( height h of triangle formed by three centres )
h = sqrt ( 2sq - 1sq ) = sqrt 3 = 1.73
Area = 4*(2+1.73) = 14.92
A simpler method: The three circles touch at a 60 degree point on each. Sin(60)=0.866. Add 1 for the radius, multiply by 2 for the lower circle: 2(0.866+1)=3.732 for the height. 3.732 X 4 = 14.928.
Good for kids
Maybe you should focus on the fact SRP is equilateral before asserting QP is the mediatrice of SR (and so QR lenght is 1)
But it's great!
Thanks Alexandre for the feedback. I thought about talking about equilateral triangle as well when I was making the video.
You are awesome 👍 Take care dear and stay blessed😃
I find 14.928 which results from 4(2+√3).
正三角形を作るのがポイントですね The key is to make an equilateral triangle.
You are right on!
Many many thanks for taking the time to leave this comment. Take care dear and stay blessed😃 You are awesome. Keep smiling😊
I agree that's how I approach it,
and of sides 2, 2, 2 hence height is sqrt 3, so the width of the rectangle is sqrt 3 +1 +1 or sqrt 3 + 2 and the length is 4.
Supper👍
Thanks Shiva dear for such an elegant feedback. Thank you so much for taking the time to leave this comment. You are awesome 👍 Take care dear and stay blessed😃
Why not dinner?
Vvnice true thanks
You are the best
Thanks for the visit! You are awesome 👍 Take care dear and stay blessed😃 Kind regards
Thank you
I Wanted To Know Of What Lesson It Is Please,
I used cos(30) :)
Right triangle
Good
4x(2+root3)
A = [(Tan 60x1) + 2] x 4 = 14.928
I used the formula to determine the height of an equilateral triangle)
#RightTriangle
A = 4(2+sqrt(3))
Answer = 4 x (1 + sq root 3 + 1) = 4 x (1 + 1.7320 + 1) = 4 x 3.7320 = 14.9280
(√3+2)4
In just 3-4 sec
#Radius
#Pythagoras #PythagoreanTheorem
1; square root of 3; 2
Is it not 16 ??
3*4= 12
Square root of 3
Pythagorean Theorem
Radius
SPQR SENATVS POPVLVSQUE ROMANVS
14.928 sq. units
Radius = 1
SuPerioR Circle diaMetre ----- radius× 4 = 4 is width / lengtH is agaiN 4 its square noT rectangle ---- area is 4 × 4 = 16 volume is 72
r = 1
Pythagoras
1+1+1+1 equals the length of all 4 sides.. the area of the square is 4 x 4...16
Thank you