Question

a triangle has two sides of lengths 7 and 9. what value could the length of the third side be? check all that apply.

a. 5
b. 10
c. 13
d. 8
e. 2
f. 22

Explanation:

Step1: Recall triangle - inequality theorem

The length of the third side \(x\) of a triangle with side lengths \(a\) and \(b\) must satisfy the inequality \(|a - b|\lt x\lt a + b\). Here \(a = 7\) and \(b = 9\).

Step2: Calculate the lower - bound

\(|7 - 9|=| - 2| = 2\), so \(x>2\).

Step3: Calculate the upper - bound

\(7 + 9=16\), so \(x<16\).

Answer:

A. 5
B. 10
C. 13
D. 8