Question

if a triangle has sides of 31 in. and 28 in., which is a possible length for the third side? (1 point)
59 in.
3 in.
33 in
62 in.

Explanation:

Step1: Recall triangle - inequality theorem

The length of the third side \(x\) of a triangle with side lengths \(a\) and \(b\) satisfies the inequality \(|a - b|\lt x\lt a + b\). Here \(a = 31\) and \(b = 28\).

Step2: Calculate the lower - bound

\(|31 - 28|=3\).

Step3: Calculate the upper - bound

\(31 + 28 = 59\). So \(3\lt x\lt59\).

Answer:

C. 33 in