Question

a crafter is making a triangular flag. she has two sides of length 24 inches and 36 inches. what are the length possibilities (in whole inches) for the third side? a 12 in. or less b 60 in. or more c between 13 in. and 59 in. d not possible

Explanation:

Step1: Recall triangle - inequality theorem

The length of the third side \(x\) of a triangle with side lengths \(a\) and \(b\) must satisfy the inequality \(|a - b|\lt x\lt a + b\). Here \(a = 24\) and \(b=36\).

Step2: Calculate the lower - bound

First, find \(|a - b|\): \(|24 - 36|=| - 12| = 12\). Since the length of a side cannot be negative, the lower - bound of the third side is \(36-24 = 12\) (but the side length must be greater than 12).

Step3: Calculate the upper - bound

Then, find \(a + b\): \(24+36=60\). The upper - bound of the third side is 60 (but the side length must be less than 60). So the length of the third side \(x\) satisfies \(12\lt x\lt60\), which means the length of the third side is between 13 in. and 59 in.

Answer:

C. between 13 in. and 59 in.