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VIC problem

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poonamchiK
 Post subject: VIC problem
 Post Posted: Sun Aug 29, 2010 2:56 am 
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Students


Posts: 104
If there are 2 corresponding angle triangles and one has an area twice the other. then in therms of s (smaller triangle's base) what is S (bigger triangle's base)
a. √ 2s /2
b. √ 3s/2
c. √2s
d. √ 3s
e. 2s

correct answer c. ?
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gokul_nair1984
 Post subject: Re: VIC problem
 Post Posted: Sun Aug 29, 2010 2:50 pm 
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Students


Posts: 170
I assume 2 corresponding angled traingles mean that 2 angles are corresponding in both triangles. Thus the third angle also has to be same. Therefore, by AAA (Angle-Angle-Angle) rule we can prove both the triangles are similar in nature.

Furthermore just by heart this rule ( It can be proven)

If two similar triangles have sides in the ratio a/b , then their areas are in the ratio (a^2)/(b^2)----(1)

Coming to the problem,
Let's assume the area of the smaller triangle is x
Therefore, the area of the larger triangle is 2x

Substituting this information in (1) we get,
(s^2)/(S^2)=x/2x

=>(s^2)/(S^2)=1/2

Therefore, S= √2s
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RonPurewal
 Post subject: Re: VIC problem
 Post Posted: Thu Sep 16, 2010 7:10 am 
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ManhattanGMAT Staff


Posts: 6765
here's a big fat existing thread on this problem:
post19973.html
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