Problem Solving

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

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

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)

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

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.

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

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.

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.

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