Question

what is the range of the third side of a triangle given sides of 38 in. and 49 in.

Explanation:

Step1: Recall triangle inequality theorem

The sum of any two sides of a triangle must be greater than the third side, and the difference of any two sides must be less than the third side. Let the third side be \( x \).

Step2: Apply the theorem

First, find the difference of the two given sides: \( 49 - 38 = 11 \). Then, find the sum of the two given sides: \( 49 + 38 = 87 \). So, the third side \( x \) must satisfy \( 11 < x < 87 \).

Answer:

The range of the third side is \( 11 \text{ in.} < x < 87 \text{ in.} \)