Question

assessment practice

1. the lengths of two sides of a triangle are 13 and 20. what is the range of values for the length x of the third side?

Explanation:

Step1: Apply the triangle inequality theorem

The triangle inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), the following must hold: \(|a - b|\lt c\lt a + b\). Let \(a = 13\) and \(b=20\).
First, calculate \(|a - b|\):
\(|13 - 20|=| - 7| = 7\)

Step2: Calculate \(a + b\)

\(13+20 = 33\)

Answer:

\(7\lt x\lt33\)