Question

select the correct answer. a triangle has one side of length 29 units and another of length 40 units. determine the range in which the length of the third side must lie. a. -11<x<69 b. 11≤x≤69 c. 11<x<69 d. -11≤x≤69

Explanation:

Step1: Recall triangle - side rule

The length of the third side \(x\) of a triangle with side lengths \(a\) and \(b\) satisfies the inequality \(|a - b|\lt x\lt a + b\). Here \(a = 29\) and \(b = 40\).

Step2: Calculate lower - bound

First, find the lower - bound: \(|40 - 29|=11\).

Step3: Calculate upper - bound

Then, find the upper - bound: \(40 + 29 = 69\). So \(11\lt x\lt69\).

Answer:

C. \(11\lt x\lt69\)