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Inscribed squares

by alex.gellatly » Tue Jul 17, 2012 9:36 pm
In the figure shown, two identical squares are inscribed in the rectangle. If the perimeter of the rectangle is 18squareroot(2,, then what is the perimeter of each square?

8squareroot2
12
12squareroot2
16
18

Note: The terrible figure is obviously not drawn to scale (sorry)
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by niketdoshi123 » Tue Jul 17, 2012 10:43 pm
alex.gellatly wrote:In the figure shown, two identical squares are inscribed in the rectangle. If the perimeter of the rectangle is 18squareroot(2,, then what is the perimeter of each square?

8squareroot2
12
12squareroot2
16
18
From the figure we can realize that the sum of the diagonal of the two squares = length of the rectangle and length of a diagonal of the square = width of the rectangle
length of diagonal of the square = d
Given 2l+2w = 18squareroot(2)
l = 2d , w = d
=> 2*2d + 2*d = 18squareroot(2)
=> d= 3squareroot(2)

d = L*squareroot(2), (L = length of the square)
=> L = 3
perimeter = 4L = 12

Hence the correct answer is B
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by Anurag@Gurome » Tue Jul 17, 2012 10:45 pm
alex.gellatly wrote:In the figure shown, two identical squares are inscribed in the rectangle. If the perimeter of the rectangle is 18squareroot(2,, then what is the perimeter of each square?
Let us assume, length of each side of the squares = a
Hence, length of the diagonals of the squares = (√2)*a

Now, length of the rectangle = 2*(the length of the diagonal of the squares) = (2√2)*a
And, width of the rectangle = the length of the diagonal of the squares = (√2)*a

Therefore, perimeter of the rectangle = 2((2√2)*a + (√2)*a) = 2*(3√2)*a = (6√2)*a

Hence, (6√2)*a = 18√2 ---> a = 3
Hence, perimeter of each square = 4a = 12

The correct answer is B.
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by GMATGuruNY » Wed Jul 18, 2012 2:45 am
alex.gellatly wrote:In the figure shown, two identical squares are inscribed in the rectangle. If the perimeter of the rectangle is 18squareroot(2,, then what is the perimeter of each square?

8squareroot2
12
12squareroot2
16
18

Note: The terrible figure is obviously not drawn to scale (sorry)
The height of the rectangle = the diagonal of each square.
The length of the rectangle = the sum of two diagonals.
Let d = the diagonal of each square.
Then the perimeter of the rectangle = 2H + 2L = 2d + 2(2d) = 6d.
Since p = 18√2, we get:
6d = 18√2
d = 3√2.
Since the diagonal of a square = s√2:
s = 3
p = 4*3 = 12.

The correct answer is B.
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