Question

multiple choice 1 point
the measures of two sides are given. between what two numbers must the third side fall.
47 and 71
0 and 118
23 and 118
24 and 95
47 and 95

Explanation:

Step1: Recall triangle - side rule

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

Step2: Calculate the lower - bound

Given \(a = 47\) and \(b = 71\), the lower - bound is \(|71 - 47|=24\).

Step3: Calculate the upper - bound

The upper - bound is \(47 + 71 = 118\). So the third side length must be between 24 and 118.

Answer:

23 and 118 (Note: Although the correct lower - bound is 24, among the given options, the option with the closest lower - bound and the correct upper - bound is "23 and 118")