Since each triangle has the same combination of angles, 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.
Smaller triangle:
Let s=1.
Thus, b = h = 1.
Area = 1/2bh = 1/2*1*1 = 1/2.
Larger triangle:
Since the larger triangle is twice as big, area = 2 * 1/2 = 1.
In the larger triangle, B = H = S.
Since the area is equal to 1, we get:
(1/2)S² = 1
S = √2. This is our target.
Now plug s=1 into the answers to see which yields our target of √2.
Only answer choice
C works:
√2s = √2*1 = √2.
The correct answer is
C.
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