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by RiyaR » Sat Oct 18, 2014 9:00 am
If ABCD is a rectangle, what is the area of the shaded region?

64

82

96

120

150
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Is the answer to this 96? I used the conceptof similarity
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by [email protected] » Sat Oct 18, 2014 11:01 am
Hi RiyaR,

Yes, you are correct. Each of the 3 triangles is [spoiler]a 3/4/5 right triangle[/spoiler].

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by j_shreyans » Sat Oct 18, 2014 10:36 pm
Hi Rich ,

Can you pls solve this?

I am using the same concept but not getting answer.
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by GMATGuruNY » Sun Oct 19, 2014 3:31 am
Let ∠ABD = x and ∠BDA = y, implying that x+y = 90.
The result is the following figure:
Image
Every triangle in the figure above has the same combination of angles:
x-y-90.
Implication:
All of the triangles are SIMILAR.
Corresponding sides in similar triangles are in the SAME RATIO.

Image
Since AB=15 and AD=20, ∆ABD is a multiple of a 3-4-5 triangle:
AB:AD:BD = 3:4:5 = 15:20:25.

Image
Since ∆BCE is similar to ∆ABD, ∆BCE must also be a multiple of a 3-4-5 triangle.
Since BC=20, we get:
CE:BE:BC = 3:4:5 = 12:16:20.
Thus, CE=12 and BE=16, implying that the area of ∆BCE = (1/2)(BE)(CE) = (1/2)(16)(12) = 96.

The correct answer is C.
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by Brent@GMATPrepNow » Sun Oct 19, 2014 12:38 pm
Image[/url]
If ABCD is a rectangle, what is the area of the shaded region?
A) 64
B) 82
C) 96
D) 120
E) 150
IMPORTANT: the diagrams in problem solving questions are DRAWN TO SCALE unless stated otherwise.

So, even though this is a tricky question, we can quickly eliminate 3 of the answer choices and have a 50-50 chance of guessing correctly. Here's how:

Rectangle ABCD has dimensions 15 x 20, so its area = 300.
So, the area of ∆BCD = 150 (half of 300)
So, the shaded area must have an area that's LESS THAN 150
So, we can eliminate E

Answer choices A and B are both APPROXIMATELY half of 150.
Does it look like half of ∆BCD is shaded?
NO.
So. we can eliminate A and B.

This leaves us with a guess between C and D

FINAL NOTE: The diagram provided here is obviously not drawn to scale, so unless there's some missing text (saying "not drawn to scale") that was supposed to accompany the diagram , this is not a GMAT-quality question.

Cheers,
Brent
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