Question

Two sides of a triangle measure 17 inches and 20 inches. Which CANNOT be the length of the remainig side?

B
37
A
7
D
20
12

Answer 1

Answer: 37

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Work Shown:

We have a triangle with sides a,b,c such that

• a = 17
• b = 20
• c = unknown

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.