similar trianlges

[brandonw3]

Two similar triangles, if the area of the bigger triangle is twice the area of the smaller triangle, then in terms of "s" (hypotenuse of smaller triangle), "S" (hypotenuse of bigger triangle)=

1) (sq root 2)/2s
2) (sq root 3)/2s
3) sq root 2s
4) sq root 3s
5) 2s

thanks

[Geisslerbg]

Make your life easy by drawing two right angle triangles with base = b, height = h and hypotenuse = s. For the bigger triangle B, H and S. Furthermore make these triangles have equal base and height to simplify the calculations.

The area of the bigger triangle = 2 x area of smaller one
2(1/2bh) = 1/2 BH
b^2 = (B^2)/2 since b=h and B=H .......equation 1

Pythagarous
S^2 = B^2 + H^2
S^2 = 2B^2
(S^2)/2 = B^2 ...........equation 2
similarly
(s^2)/2 = b^2 ............equation 3

Substitute eq 2 and eq 3 into eq 1 above
(s^2)/2 = (S^2)/2/2
2(s^2) = (S^2)
S=(sq root 2)s
Formula still holds if triangle is not isosolese this just easier to work with

[Stuart@KaplanGMAT]

The actual question has diagrams - and has been answered many times on this forum.

Here's one thread:

https://www.beatthegmat.com/geometry-t11659.html