Question

two sides of a triangle have lengths 21 and 37. which inequality describes the possible lengths of the third side? 21 < x < 57 21 ≤ x ≤ 37 16 ≤ x ≤ 58 16 < x < 58

Explanation:

Step1: Apply triangle - side inequality

The triangle - side inequality states that for a triangle with side lengths \(a\), \(b\), and \(c\), \(|a - b|\lt c\lt a + b\). Let \(a = 21\) and \(b = 37\).
First, calculate \(b - a\):
\(37-21=16\)
Second, calculate \(a + b\):
\(21 + 37=58\)

Answer:

\(16\lt x\lt58\)