Since each triangle has the same combination of angles, we know that the triangles are similar. The combination of angles is not specified, so we can plug in our own values.

Let each triangle be a 45-45-90 triangle so that the sides are proportioned x : x : x√2.

Plug in s=1.
Thus, in the smaller triangle, b = h = 1.
Area = 1/2bh = 1/2*1*1 = 1/2.

Since the larger triangle is twice as big, larger area = 2*1/2 = 1.
In the larger triangle, B = H = S.
Thus, A = 1/2BH = (1/2)S² = 1.
Thus, S = √2. This is our target.

Now we plug s=1 into all the answers to see which yields our target of √2.

Only answer choice C works:
√2s = √2*1 = √2.

The correct answer is C.

ithamarsorek wrote: .....

area small triangle t=s*h/2
area big triangle T=S*H/2
property of similar triangles = s/S=h/H (EQ.1) --> S=H*s/h

T=2t --> S*H/2=2s*h/2 --> S*H=2s*h (EQ.2) --> S=2s*h/H

Combine and solve two equations: EQ.1 and EQ.2 --> H*s/h=2s*h/H --> H*s*H=2s*h*h (cancel s on both sides) --> H^2=2*h^2 --> H=Sqrt(2)*h
S=H* s/h OR S=Sqrt(2)*h*s/h=Sqrt(2)*s

answer C