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GMAT Prep: Similar Triangles

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Senior Manager
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GMAT Prep: Similar Triangles [#permalink]  06 Dec 2005, 13:19
Can someone please explain how to work this. Thanks.

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Intern
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In similar triangles, all dimensions are in proportion.

A = s*h/2 for smaller triangle
A = S*H/2 for larger triangle

2*s*h/2 = S*H/2 b/c stem says that twice the smaller area equals the larger triangles area.

Simplify and s = 0.5*S*H/h

Now b/c they are similar s/S = h/H or S/s = H/h, plug this in and you will see that s = sqrt(2)*S/2
Senior Manager
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Good explanation, thanks
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Intern
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well there's another explanation: Since we are not told whether the triangles are equlateral or not...suppose them to be equilateral...
=>the area of the larger triangle is {sqrt(3)*S^2}\4
similarly for the smaller it turns out to be {sqrt(3)*s^2}\4
but 2*{sqrt(3)*s^2}\4={sqrt(3)*S^2}\4

Which on simplification gives option C.
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