Question

a triangle has two sides of length 18 and 6. 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 \(a = 18\) and \(b=6\). Then \(|18 - 6|\lt c\lt18 + 6\), which simplifies to \(12\lt c\lt24\).

Step2: Find the smallest whole - number

Since \(c\) must be a whole number and \(c>12\), the smallest whole - number value of \(c\) is \(13\).

Answer:

\(13\)