Question

sharel wants to draw a triangle with side lengths of 17 millimeters and 15 millimeters. what is the range of possible lengths for the third side that she can use? write your answer as a compound inequality using x.

Explanation:

Step1: Apply triangle inequality theorem

Let the third side be \(x\). According to the triangle - inequality theorem, for a triangle with side lengths \(a\), \(b\), and \(c\), \(|a - b|\lt c\lt a + b\). Here \(a = 17\) and \(b=15\).
First, find \(a - b\): \(17-15 = 2\).
Second, find \(a + b\): \(17 + 15=32\).

Answer:

\(2\lt x\lt32\)