mjjking-
I'll try to break down what Alara533 wrote, but it's pretty clear. So, you might need to be more specific on your confusion.
Similar triangles have the same interior angles and their lengths are all proportional by the same factor (as Alara wrote "k"). This tells us:
ks=S (side s of the small triangle * a number k is equal to side S of the large triangle)
kh=H (height h of the small triangle * a number k is equal to height H of the large triangle)
The initial statement tells us that the proportion of the AREAS is 2. Don't confuse this with the proportion of the sides.
The area of the smaller triangle is A=(1/2)bh. Since the b ("base") equals "s", we can state A=(1/2)sh.
The larger triangles area is A=(1/2)bh. The "base" is "S". And the height is "H" (I'm simply stating that the second triangles height is different from the smaller "h" of the small triangle).
Since the intial question tells us that the larger similar triangle is twice the AREA of the smaller similar triangle, we can set our two areas equal to each other as such:
2*((1/2)*s*h)=(1/2)*ks*kh
When you factor the right side, you get:
2*((1/2)*s*h)=((1/2)*s*h)*k^2
Divide (and remove) (1/2)*s*h) from each side, and you are left with:
2=k^2
Take the sqrt of each side, and you have:
k= sqrt 2
Since S= k * s, S= sqrt (2) * s.
Hope that helps clarify.
