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by f2001290 » Tue Jun 12, 2007 7:04 am
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
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by gmatfan » Tue Jun 12, 2007 7:22 pm
Because the squares are in the rectangle diagonally, the length is two diagonals, and the width is one, or basically L=2W.

The formula for perimeter is 2L+2W, so 2L+2W=18*root 2.

Plugging in 2W for L gives 2(2W)+2W=18*root 2
4W+2W=18*root 2
6W=18*root 2
W=3*root2

Knowing that the diagonal of the square is 3*root2, and that the sides of a 45 degree triangle are x, x, and x*root2 for the hypotenuse means the side of the square is 3.

Thus, the perimeter of one square is 4*3, or 12.

Is that the OA?
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by chaitrabhat » Tue Jun 12, 2007 9:42 pm
12
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by f2001290 » Wed Jun 13, 2007 1:11 am
(18 by sqrt2) is 18*sqrt2 or 18/sqrt2 ????
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by gmatfan » Wed Jun 13, 2007 10:56 am
18 by square root of 2 is 18*root 2. Just like 2 by 4 is 2*4.

That's how I interpret it.
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