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

The length of the third side \(x\) of a triangle with two side lengths \(a\) and \(b\) satisfies the inequality \(|a - b|\lt x\lt a + b\).

Step2: Calculate the lower - bound

Given \(a = 35\) and \(b = 19\), then \(|35 - 19|=16\).

Step3: Find the smallest whole - number

Since \(x\gt16\), the smallest whole - number value for \(x\) is 17.

Answer:

17