Question

given 43 and 62 as the lengths of two sides of a triangle, find the range of values for the third side. 19 < x < ? enter the number that belongs in the green box.

Explanation:

Step1: Recall triangle - inequality theorem

The length of the third side \(x\) of a triangle with side lengths \(a\) and \(b\) satisfies \(|a - b|\lt x\lt a + b\). Here \(a = 62\) and \(b = 43\). We already have the lower - bound \(|62 - 43|=19\).

Step2: Calculate the upper - bound

We find the upper - bound by adding the two given side lengths. So \(x\lt62 + 43\).
\(62+43 = 105\)

Answer:

105