Question

in triangle xyz, the length of side xy is 25 mm and the length of side yz is 35 mm. which of the following could be the length of side xz? a. 62 mm b. 8 mm c. 65 mm d. 39 mm

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let \(a = 25\), \(b = 35\), and \(c\) be the length of the third - side \(XZ\). Then \(a + b>c\), \(a + c>b\), and \(b + c>a\). Also, \(|a - b|

Step2: Calculate the range of the third - side length

First, calculate \(a + b\) and \(|a - b|\). \(a + b=25 + 35=60\) and \(|a - b|=|25 - 35| = 10\). So, \(10

Answer:

D. 39 mm