2 triangles

Imagine they were 2 squares. Area of smaller one is 2 incehes squared and Area of bigger one would be 4 inces squared. So side of the bigger square would be 2 and the sides of the smaller square would be root 2. Same principle but with triangles.

Or you can say it this way. If you increase the dimensions of a triangle by a factor of 2 then the area increases by a factor of 4. Therefore to increase the area by a factor of 2 you must increase the dimensions by a factor of root 2. coz root 2 squared is 2.

Consider H as height of S and h as height of s
Since S and s triangles are similar,
So,
H/S = h/s
Therefore, H/h = S/s or h/H = s/S

A(triangle S) = 2 A(triangle s)
therefore, 1/2 * S * H = 1/2 * s * h

ie. S = 2 * s * (h/H)
= 2 * s * (s/S)
S^2 = 2 * s^2
Taking root
S = Root(2) * s

Thus, the answer

HTH,
syr