Question

given that two sides of a triangle are 3 in and 8 in. which of the following lengths could be the length of the third side of the triangle. (choose all that apply)
4 in 7 in 9 in 10 in
5 in 8 in 6 in 15 in

Explanation:

Step1: Recall triangle - inequality theorem

The length of the third side \(x\) of a triangle with two side - lengths \(a\) and \(b\) satisfies \(|a - b|\lt x\lt a + b\). Here \(a = 3\) and \(b = 8\).

Step2: Calculate the lower and upper bounds

First, calculate \(|3 - 8|=| - 5| = 5\) and \(3+8 = 11\). So, \(5\lt x\lt11\).

Answer:

7 in, 9 in, 10 in, 8 in, 6 in