Question

a triangle has two sides of length 17 and 1. what is the smallest possible whole - number length for the third side?

Explanation:

Step1: Recall triangle - inequality theorem

The difference between the lengths of two sides of a triangle is less than the length of the third side. Let the sides of the triangle be \(a = 17\), \(b = 1\), and \(c\) be the third - side. Then \(|a - b|\lt c\lt a + b\).

Step2: Calculate the lower - bound

We calculate \(|17 - 1|=16\). Since \(c\gt|a - b|\), and \(c\) is a whole number, the smallest whole - number value of \(c\) that satisfies the inequality \(c\gt16\) is \(17\).

Answer:

17