Question

a triangle has two sides of length 20 and 7. what is the smallest possible whole - number length for the third side?

Explanation:

Step1: Apply triangle inequality theorem

The triangle inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), \(|a - b|\lt c\lt a + b\). Let \(a = 20\) and \(b=7\). Then \(|20 - 7|\lt c\lt20 + 7\), which simplifies to \(13\lt c\lt27\).

Step2: Find the smallest whole - number

Since \(c\) must be a whole number and \(13\lt c\), the smallest whole - number value of \(c\) is \(14\).

Answer:

\(14\)