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# In the figure shown above, two identical squares are

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Manager
Joined: 28 Aug 2006
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In the figure shown above, two identical squares are [#permalink]  09 Jun 2007, 18:52
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In the figure shown above, two identical squares are inscribed in the rectangle. If the perimeter of the rectangle is 18 by squareroot2, then what is the perimeter of each square?

(A) 8 by squareroot2
(B) 12
(C) 12 by squareroot2
(D) 16
(E) 18

OA will be posted next day
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Director
Joined: 26 Feb 2006
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Re: perimeter of each Square?? [#permalink]  09 Jun 2007, 19:16
humtum0 wrote:
In the figure shown above, two identical squares are inscribed in the rectangle. If the perimeter of the rectangle is 18 by squareroot2, then what is the perimeter of each square?

(A) 8 by squareroot2
(B) 12
(C) 12 by squareroot2
(D) 16
(E) 18

OA will be posted next day

B.
side of each square = x
diagnol of the square = hight of the rectangle = x sqrt(2)
length of the rectangle = 2 x sqrt(2)
perimeter of the rectangle = 2 [2 x sqrt(2) + x sqrt(2)]
18 sqrt(2) = 2 [2 x sqrt(2) + x sqrt(2)]
x = 3
perimeter of each square = 12
CEO
Joined: 17 May 2007
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The answer is B - 12.

The key to understanding this problem is understanding that the length of the rectangle is twice the height (since 2 identical square are inscribed in it).

then its simple 2(2*h+ h ) = 18sqrt(2)
3h = 9sqrt(2)
h = 3sqrt(2)

Now h is also a diagonal of one of the squares.
if the length of the side of the square were x then according to isosceles triangle rule x + x = 3 sqrt(2) which means x = 3. For each inscribed square perimeter = 3 * 4 = 12. Hence option B.

ps. I am working under the assumption that "perimeter of the rectangle is 18 by squareroot2" implies 18*sqrt(2) not 18/sqrt(2). If I used 18/sqrt(2) I wouldnt get an answer in the selection.
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