Answer: 37
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Work Shown:
We have a triangle with sides a,b,c such that
The third side c can be represented by this inequality
b-a < c < b+a
which is a modified form of the triangle inequality theorem.
Plug in the given values to get
b-a < c < b+a
20-17 < c < 20+17
3 < c < 37
The third side length is between 3 and 37; it cannot equal 3, and it cannot equal 37. So we exclude both endpoints.
Of the answer choices, the values {7,20, 12} are in the range 3 < c < 37.
The value c = 37 is not in the range 3 < c < 37 because we can't have the third side equal to either endpoint. Otherwise, we get a straight line instead of a triangle forming.
So that's why 37 is the only possible answer here.