Question

1. if a triangle has lengths of 27 m and 11 m, select 2 possible lengths for the third side. 13 16 17 35 40

Explanation:

Step1: Recall triangle - inequality theorem

Let the sides of the triangle be \(a = 27\), \(b = 11\), and \(c\) be the third - side. The triangle - inequality theorem states that \(|a - b|\lt c\lt a + b\).

Step2: Calculate the lower and upper bounds

First, calculate \(|a - b|\): \(|27-11|=16\). Then, calculate \(a + b\): \(27 + 11=38\). So, \(16\lt c\lt38\).

Answer:

C. 17, D. 35