Another weird GMAT Question? Can't afford a Kaplan Course:(?

Question

Thanks guys. Some of these answers are flawless. I mean I really get it. That being said:

This question has a picture of two triangles side by side. There are no degree measures nor angles given, and the smallest triangle is located on the left.

The base of the smallest triangle is labeled "s." and the base of the largest triagle is labeled "S"

Question:
In the figure above, if the area of the triangle on the right is twice the area of the triangle on teh left, then in terms of s, S =?

Answer 1

Assumption
Both the triangle are equilateral.
now,
Let area of the bigger triangle be A1 & smaller triangle be A2
Let base of larger triange is S & smaller triange is s

In a equilateral triangle, height is sqrt (2) x base

for larger triangle, height = sqrt 2 * S
for smaller triange, height = sqrt 2 * s

From the data, it is clear that

A1 = 2A2

therefore

1/2*sqrt 2 * S *S= 2(1/2 sqrt 2 * s)*s

S*S = 2*s*s

S = sqrt 2*s

Answer 2

if the area of the triangle on the right is twice the area of the triangle on teh left : it means 1:2
so in terms of s S it means 1:root 2

for exp:
if the area would be 1:9
in terms of s S it would be 1:3

Answer 3

The area of the left triangle is 1/2*s*h1, where h1 is the triangle's height.

The area of the right triangle is 1/2*S*h2, where h2 is that triangle's height.

Since 1/2*S*h2=2*(1/2)*s*h1, it follows that

S=2*(1/2)*s*h2 / [(1/2)*h2] = 2*s*(h2/h1).

If the picture indicates that the triangles are the same height, then you can say that S=2s.

Answer 4

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Answer 5

Area of a triangle = bh/2
height of the small triangle = h1, height of the large traingle = h2,
Area of the small triangle = s(h1)/2
Area of the large traingle = S(h2)/2
We also know that
S(h2)/2 = s(h1)
S = (2s[h1])/(h2)

Answer 6

The area of the small triangle is a = 0.5sh
The area of the big triangle is A = 0.5SH

According to your statement, A = 2a
So,

0.5SH = 2(0.5sh)
0.5SH = sh

Now isolate S.
S = (sh)/ (0.5H)