Question

teacher:stirewalt class:1st period math 2 spring 2025 lee4tvsp
student gentry, holden
describe the possible lengths for the third side of a triangle with two sides of 6 in and 9 in using a compound inequality. (hint: use < or > to submit your answer.)

Explanation:

Step1: Recall triangle - inequality theorem

The length of the third side \(x\) of a triangle with side lengths \(a\) and \(b\) satisfies the following two inequalities: \(|a - b|\lt x\lt a + b\).

Step2: Identify \(a\) and \(b\) values

Let \(a = 6\) and \(b = 9\). First, calculate \(|a - b|\): \(|6 - 9|=| - 3| = 3\). Then calculate \(a + b\): \(6+9 = 15\).

Answer:

\(3\lt x\lt15\)