The lengths of three sides of a triangle are 5, 9, and X, all measured in centimeters. What are all the possible values of X?

Question

A. 4 < x < 14

B. 0 < x < 14

C. 5 < x < 15

D. 3 < x < 9

Answer 1

The length of any one side of a triangle is always less than the sum of the lengths of the other two sides.

Because the other two sides are 5 and 9, which sums to 14, X has to be less than 14.

The side length 9 has to be less than the sum of the side lengths 5 and X.

9 < 5 + x

4 < x

So x has to be between 4 and 14, non-inclusive. (A)