Since there is a variable in the answer choices, we can plug in.
The two triangles are similar.
We should choose a type of triangle whose characteristics are familiar.
Let each triangle be a 45-45-90 triangle.
∆ABC:
Let s=1.
A = (1/2)(1)(1) = 1/2.
∆DEF:
Since ∆DEF is twice the size, A=1.
Thus:
(1/2)(S)(S) = 1.
S²= 2.
S = √2. This is our target.
Now we plug s=1 into the answers to which yields our target of √2.
Only answer choice C works:
(√2)s = (√2)(1) = √2.
The correct answer is C.
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