similar trianlges

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

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