Three identical squares are inscribed within a rectangle as shown abov

Question

https://gmatclub.com/forum/download/file.php?id=65506 Three identical squares are inscribed within a rectangle as shown above. If the area of the rectangle is 216, what is the area of one of the squares? A. 36 B. 36\sqrt{2} C. 54 D. 54\sqrt{2} E. 72 Project PS Butler Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS 1.png

desertEagle · Answer

Cut the rectangle in three parts. Now fold the triangles in the inner square. We observe that the 4 outer triangles will make one inner square. 
So, one big square will form 2 smaller squares. There are 3 such squares. So a total of 6 such squares will be formed.

Area of each square will be equal to area of rectangle divided by 6 = 216/6= 36

Ans A

parth04red · Answer

https://gmatclub.com/forum/download/file.php?id=65506 
Three identical squares are inscribed within a rectangle as shown above. If the area of the rectangle is 216, what is the area of one of the squares?

A. 36

B.  36\sqrt{2} 
 
C. 54
 
D.  54\sqrt{2} 
 
E. 72

take a look at the image.
I've leveraged the fact that a triangle with same base and height as a parallelogram covers half the area.
we can divide the rectangle into 2 equal parts.
each part will have 3 identical triangles(half of the each identical inscribed square)
this means the 3 identical squares cover half the area of the rectangle.
area 3 squares = 216/2
 = 108
hence, area of 1 square = 108/3
 = 36.
answer should be option A.

let me know if you have any queries.
hopefully i didnt miss out any key information.
cheers

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accountingnerd30 · Answer

My approach

Area of rectangle = LB
216= LB.

From figure we can infer B= Diagonal of small square and L= diagonal of square*3 (because 3 square are placed above one another) Let diagonal of square be x so we can say LB=3x*x

Hence 216=3x*x
216= 3x^2
216/3= x^2
72=x^2
36* 2=x^2
6 root 2= x

Diagonal of square is root2*side of square (Property)

Hence we can say side of square is 6 and hence area of square will be 6 square = 36

Experts let me know if anything wrong with my approach.

Thanks.

Pastillita · Answer

Hey, this is pretty similar to what I did, I noted that the area of 216 = L*W, where L = 3*diagonal of square and W= 1*diagonal of square.

We know that the diagonal of a square has a length of x*root(2); where 'x' = the length of a side of the square. This is a general rule as when you cut a square from its diagonal it forms a 45-45-90 triangle with legs of length 'x' (same as the sides of the square) and a hypotenuse of x*root(2).

Hence the L = 3*x*root(2) and W = x*root(2)

Therefore, the area of the rectangle can be expressed as L*W = (3*x*root(2))*(x*root(2)) = 216

So 6x^2 = 216 thus x = 6 (where 'x' is a side of the square); so Area of a square = 6*6 = 36

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Three identical squares are inscribed within a rectangle as shown abov

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