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Similar triangles

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Similar triangles

by anshul265 » Mon Apr 14, 2008 4:20 pm
All,

Can some one please solve this question for me. Its a similar triangle problem which was on test 2 of the official gmat.

Either there is a simple property of triangles (similar triangle) that I dont know off , or this is surely a difficulty level 5 question.

Thanks,
-Anshul
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by khurram » Mon Apr 14, 2008 6:41 pm
which is the answer. C or e

I would have guessed 2s as 1/2 *b*h=b*h of bigger if the area of bigger is twice that of smaller.

So in terms of smaller s1, big s would be just twice 2s.

Khurram
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by mmukher » Mon Apr 14, 2008 8:03 pm
The answer is C.

I had to google this one.
https://www.mathwarehouse.com/geometry/s ... angles.php


Essentially for similar triangles

Ratio of Areas = square ( Ratio of sides )


Here ratio of areas is given as 2, therefore ratio of sides is sqrt(2)
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by anshul265 » Mon Apr 14, 2008 8:30 pm
Aha !! Thanks ...

The correct answer is indeed C.

But seriously they expect us to know "THIS" property of similar triangles. Just glad , that no one knew this at the top of their head and i wasnt missing on something too obvious.

Thanks again!!
-A
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by khurram » Mon Apr 14, 2008 8:35 pm
makes sense

I know that if area is 4 times larger, then sides are twice as big, so square of 2 is 4, so area is twice as big so square of 2 wil give ratio of sides.
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by mandy12 » Mon Apr 14, 2008 8:48 pm
A simple thing to keep in mind is that the ratio of sides for similar traingles is same. So in the given question ...Area of larger traingle is twice i.e.

1/2SH = 2*1/2sh

=> SH = 2*sh (where H is the height of big tr and h is height of smaller one)

Also as they are similar trs

S/s = H/h => H = S*h/s

Putting this value of H in the above equation ..u get S = sqrt2*s
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by khurram » Mon Apr 14, 2008 9:01 pm
makes sense

I know that if area is 4 times larger, then sides are twice as big, so square of 2 is 4, so area is twice as big so square of 2 wil give ratio of sides.
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by Stuart@KaplanGMAT » Tue Apr 15, 2008 11:40 am
Remember... area is a square function, length is linear.

So, if you double all the lengths, you'll 2^2 = quadruple the area. If you triple all the lengths, you'll 3^2 = nontuple (no clue if that's a real word, by the way!) the area.
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s/S = h/H

by netigen » Tue Apr 15, 2008 3:02 pm
What helps is that all sides and height across the 2 triangles have the same ratio, which means that in this case

s/S = h/H

h = height of smaller triangle
H = height of larger triangle

This helps solve the problem
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