help

Hi sana.noor,

In the drawing that you provided, you should notice that:

the width of the rectangle = 2(square's diagonal)
the height of the rectangle = 1(square's diagonal)

Using square "rules", the diagonal = x(root2)

So the area of the rectangle = (width)(height) = 2(x(root2))^2 = 36

Let's simplify:
(x(root2))^2 = 18
x^2(2) = 18
x^2 = 9
x = 3

So the perimeter of each square = 3(4) = 12

GMAT assassins aren't born, they're made,
Rich

sana.noor wrote:

In the figure shown, two identical squares are inscribed in the rectangle. If the area of the rectangle is 36, what is the perimeter of each square?

Here's a slightly different approach:
Since the height of the rectangle and the diagonal of a square are the same length, let's let x = height of rectangle


Since the width of the rectangle is equal to the length of two square diagonals, then the width of the rectangle = 2x.


The area of the rectangle is 36.
So, (base)(height) = 36
(2x)(x) = 36
2x²= 36
x²= 18
x = √18

NOTE: There's no need to simplify √18 at this point (you'll see why shortly)

If the height of the rectangle is √18, then the length of the red line (shown below) must equal √18/(2)


Likewise, the other red line has length √18/(2)


If we let y = the length of the hypotenuse, then the Pythagorean Theorem states that...


Now solve this equation for y.


If y = 3, then the perimeter of one square = (4)(3) = 12

Cheers,
Brent

Hi happy888,

The 'key' to this whole question is in realizing that the width and height of the rectangle can be expressed in terms of the DIAGONAL of each of the SQUARES. Are you able to follow the 'set-up' of the calculations involved?

GMAT assassins aren't born, they're made,
Rich

happy888 wrote:Hi Brent,

I didn't understand why 1/4th length of the rectangle is squareroot18/2

Thanks

Once we know that the height of the rectangle is √18, then HALF of that is (√18)/2


I hope that helps.

Cheers,
Brent

The squares just take up half the rectangle. There are a few ways to see that. For example, if you divide up the picture into a grid of 8 squares, as I did below, you can see that half of each grid zone is taken up by part of a square, and the other half is taken up by non-square.

So the area of the squares is half the total area of the rectangle, so the area of the two squares is 36/2 = 18, and the area of each square is 9. So the squares measure 3 by 3, and the perimeter of each is 12.