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by ketkoag » Sat May 16, 2009 1:39 am
In the figure attached with this post, 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

please lemme know if the answer to this question is 6
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by DanaJ » Sat May 16, 2009 2:17 am
I have a feeling that this question has been answered before, but here goes:

Notice that the perimeter = 2(length + width).

Now, let's break each one of those based on our rectangles.
The length is the sum of diagonals and since the squares are identical, the length will be 2*diagonal. Say the side of a small square is x. This makes the diagonal x*sqrt(2) (it's that formula for the diagonal of a square), so the length of the rectangle will be 2x*sqrt(2).

On the other hand, the width is just one diagonal long, so width = x*sqrt(2).

The perimeter will be 18sqrt(2) = 2(x*sqrt(2) + 2x*sqrt(2)).

9sqrt(2) = 3xsqrt(2)

x = 3. Since the squares have sides of 3 each, the perimeter will be 4*3 = 12.
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by dadagreat » Sat May 16, 2009 3:24 am
I got the answer as 6. DanaJ - from the problem, i read the perimeter of the rectangle as 18/sqrt(2). You have assumed 18*sqrt(2).

18/sqrt(2) = 2(x*sqrt(2) + 2x*sqrt(2))

So if i change your equation as above, x works out to as 1.5 and perimeter as 6.
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by ketkoag » Sat May 16, 2009 10:25 am
thanks for ur responses.....
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