Problem Solving

kwah wrote:Attached is a question from GMAT Prep Test 2.

Please advise how to achieve the result.

Answer: C

Thanks,
K

Since the angles of two triangles are same, so the triangles are similar triangles.
Also, area of the triangle on the right is twice the area of the triangle on the left.

Area of triangle = (1/2) * base * height
Let us assume that height of bigger triangle = H and height of smaller triangle = h
Then area of small triangle = (1/2) * s * h, and
area of bigger triangle = (1/2) * S * H

So, (1/2) * S * H = 2 * (1/2) * s * h
(1/2) * S * H = s * h
Since the triangles are similar, so the sides facing the equal angles are always in the same ratio. So, S/s = H/h

So, (1/2) * S * (S/s) = s or S² = 2s²
S = [spoiler]s√2[/spoiler]

The correct answer is C.