Question

a triangle has two sides of length 35 and 19. what is the smallest possible whole - number length for the third side?

Explanation:

Step1: Recall triangle - inequality theorem

Let the sides of the triangle be \(a = 35\), \(b = 19\), and \(c\) be the third - side. The triangle - inequality theorem states that \(|a - b|\lt c\lt a + b\).

Step2: Calculate the lower - bound

First, find \(|a - b|\). We have \(|35−19|=|16| = 16\). Since \(c\) is a whole number and \(c\gt|a - b|\), the smallest whole - number value for \(c\) is \(17\).

Answer:

17