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each side of square ABCD has length 1, the length of line

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each side of square ABCD has length 1, the length of line [#permalink] New post 20 Nov 2008, 08:12
each side of square ABCD has length 1, the length of line
Segment CE is 1, and the length of line segment BE is equal to the length
Of line segment DE. What is the area of the triangular region BCE?
a. 1/3 b. (2^-2 )/4 c. 1/2
d. (2^-2)/2 e. 3/4
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Re: square ABCD--25 [#permalink] New post 22 Nov 2008, 05:49
Hi
The answer to this question is b. (2^-2 )/4. :)
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Re: square ABCD--25 [#permalink] New post 23 Nov 2008, 22:36
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line segment BC = line segment DC
BE=DE(given)
and CE is common between triangles CDE and BCE.so they are similar.
= <DCE = <BCE = 45 or point E lies on the diagonal.

so area of triangle BCE = BC * CE *sin(45)/2

=> 1/(2*sqrt(2)) = sqrt(2)/4

answer b
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Re: square ABCD--25 [#permalink] New post 24 Nov 2008, 01:08
emailsector, gmat isn't testing knowledge of trigonometric formulas, so there is always other ways to get a right answer. I'm also getting 1/2sqrt2 = sqrt2/4, but it isn't among answer choices for b = 2^-2/4 = 1/16, which is impossible. So, I think there is a mistake in the answer choices.

My solwing way: from E draw a perpendicular line to BC and call it EF. Angle EFC = 90, FCE = 45 = FEC. So, with given EC = 1 we get EF = 1/sqrt2 (45:45:90 => 1:1:sqrt2). Area of EFC = 1/2 x 1 x 1/sqrt2 = 1/2sqrt2 = sqrt2/4.
Re: square ABCD--25   [#permalink] 24 Nov 2008, 01:08
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each side of square ABCD has length 1, the length of line

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