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: Apply triangle inequality theorem

The triangle inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), \(|a - b|\lt c\lt a + b\). Let \(a = 40\) and \(b=29\).

Step2: Calculate \(|a - b|\)

\(|40 - 29|=11\)

Step3: Calculate \(a + b\)

\(40 + 29 = 69\)

Step4: Determine the range of the third side \(x\)

Since \(|a - b|\lt x\lt a + b\), substituting the values of \(a\) and \(b\) gives \(11\lt x\lt69\)

Answer:

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