Question

a triangle has two sides of length 3 and 6. what is the smallest possible whole - number length for the third side?

Explanation:

Step1: Recall triangle - inequality theorem

The length of the third side \(x\) of a triangle with side lengths \(a\) and \(b\) must satisfy the inequalities \(|a - b|\lt x\lt a + b\). Here \(a = 3\) and \(b = 6\).

Step2: Calculate the lower - bound

First, calculate \(|a - b|\). Since \(|3 - 6|=| - 3| = 3\). The inequality for the third - side length \(x\) is \(3\lt x\lt3 + 6=9\).

Step3: Find the smallest whole - number

The smallest whole number greater than 3 is 4.

Answer:

4