Question

a triangle has two sides of length 2 and 11. 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 \(a = 2\) and \(b=11\). Then \(|11 - 2|\lt c\lt11 + 2\), which simplifies to \(9\lt c\lt13\).

Step2: Find the smallest whole - number

Since \(c\) must be a whole number and \(9\lt c\), the smallest whole - number value of \(c\) is \(10\).

Answer:

\(10\)