Question

the measures of two sides are given. between what two numbers must the third side fall. 9 and 15
0 and 24
3 and 21
6 and 24
9 and 21
6 multiple choice 1 point
the measures of two sides are given. between what two numbers must the third side fall. 5 and 8
0 and 13
3 and 13
9 and 22
5 and 18

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: Solve for the first case (\(a = 9\), \(b = 15\))

First, calculate \(|a - b|=|9 - 15| = 6\) and \(a + b=9 + 15=24\). So the third - side length is between 6 and 24.

Step3: Solve for the second case (\(a = 5\), \(b = 8\))

Calculate \(|a - b|=|5 - 8| = 3\) and \(a + b=5+8 = 13\). So the third - side length is between 3 and 13.

Answer:

1. C. 6 and 24
2. B. 3 and 13