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Help in Solving problem.

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Junior | Next Rank: 30 Posts
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by xunil56 » Sat Sep 06, 2008 5:02 pm
Hi,

I could not search for this problem give the nature of the diagram. So I am hoping that I am not repeating this questions.

In the attached image, how would I find the area of the shaded region.

The answers given were:
1) 64
2) 82
3) 96 -- This is the correct answer.
4) 120
5) 150

What I am looking is for a way to solve this problem?

Thanks in Advance.
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Its very simple one..

by karthikgmat » Sat Sep 06, 2008 10:31 pm
in the diagram area of rectangle= 15*20
half area of rectangle is triangle BCD ar(BCD)= 150
and Tr(BCE) and Tr(CED) are right angle triangle so
BE^2 + EC^2 = 20 ^2 (pythogaros theroem)
similarly DE^2 + EC^2 = 15 ^2 and remember BE+ED= 25
so we get ED =9
and EC = 12


so area of TR(BEC) = 1/2 * 12 * 16 =96 sq.units.
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by Ian Stewart » Sun Sep 07, 2008 8:34 am
Or you can notice that all of the triangles are similar (label the angles and you'll see each triangle has the same set of angles). The largest triangle is a

15-20-25 triangle (5 times bigger than a 3-4-5)

The other triangles' sides are in the same ratio; their sides are:

9-12-15 (three times a 3-4-5)
12-16-20 (four times a 3-4-5)

We want the area of the 12-16-20 triangle, which is 12*16/2 = 96.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
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