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by mpaudena » Tue Feb 17, 2009 8:00 pm
Okay, here is a question from the GMAT software test. I couldn't copy and paste the image so please bare with me as I describe the image; it's pretty simple:

Two triangles - one appears larger than the other, but the question says that the figures are not drawn to scale. The angles of triangle 1 and triangle 2 are labelled x, y, and z indicating that the triangles have congruent angles. On the small triangle there is a side that is labelled "s" and on the large triangle the corresponding side is labelled "S."

Now the question:

In the figures above, if the area of the larger triangle is twice the area of of the smaller triangle, then in terms of s, S =

A) (square root of 2/2)s

B) (square root of 3/2)s

C) (square root of 2)s

D) (square root of 3)s

E) (2)s
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Source: — Problem Solving |

by tini » Tue Feb 17, 2009 8:10 pm
I just solved it yesterday. Its very simple. You should know the property of similar triangles. If two triangles are similar then their areas are in proportion to the square of the sides.

the triangles are similar as per AAA property:

so area of the triangle with side S/area of the triangle with side s = (S/s)^2

So, (S/s)^2=2 (as per the question area of the triangle with side S is twice the area of the other)

so , S= sqrt2s
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by mpaudena » Wed Feb 18, 2009 7:41 am
tini wrote:I just solved it yesterday. Its very simple. You should know the property of similar triangles. If two triangles are similar then their areas are in proportion to the square of the sides.

the triangles are similar as per AAA property:

so area of the triangle with side S/area of the triangle with side s = (S/s)^2

So, (S/s)^2=2 (as per the question area of the triangle with side S is twice the area of the other)

so , S= sqrt2s
Thanks for the response but you lost me. What does AAA property mean? Also, I don't understand why (S/s) is squared. The question says S = 2s so shouldn't it be S/s = 2? Thanks.
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by tini » Wed Feb 18, 2009 7:46 am
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by tini » Wed Feb 18, 2009 7:48 am
also refer to :
https://www.onlinemathlearning.com/simil ... es.html#aa

AA is a rule to prove that two triangles are similar
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