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DS: Square Rectangle

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Director
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DS: Square Rectangle [#permalink] New post 14 Dec 2004, 07:15
00:00
A
B
C
D
E

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(N/A)

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0% (00:00) correct 0% (00:00) wrong based on 0 sessions

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 [#permalink] New post 14 Dec 2004, 08:02
The answer is "D".
Stat(1): AC=EG. Let EG=x. then EH=x/sqrt(2). AB=x/2(sqrt2).With this we can find the side BC(one side of the rectangle and the diagonal are known).Hence we can find the area in terms of 'x'. Hence suffic.
Stat(2): As the diagonal divides both into two equal parts, if area of triangles is not same, then definitely the areas of rectangles are not same.
Hence suffic....
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DS: Square Rectangle [#permalink] New post 14 Dec 2004, 08:34
I agree with Gladiator: D, with the same reasoning.
For 1, I did EG=sqrt(2), so EH=1, and AB=1/2 AC=sqrt(2). The rectangle is 7/8 the area of the square

2 is obvious, if the area of triangles are not equal, twice the area of each is not going to make them equal
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 [#permalink] New post 14 Dec 2004, 11:11
agreed. I choose D.

one thing: I did this by plugging in numbers. The square is a perfect figure, and the rectangle's side is half the square, so I knew that by plugging in just one value I'd get a very good idea of what's happening in the problem. Once I did, I saw everything clearly.
  [#permalink] 14 Dec 2004, 11:11
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DS: Square Rectangle

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