Question

question 10 of 10
a triangle has sides measuring 2 inches and 7 inches. if x represents the length in inches of the third side, which inequality gives the range of possible values for x?
a. 2 < x < 7
b. 2 ≤ x ≤ 7
c. 5 < x < 9
d. 5 ≤ x ≤ 9

Explanation:

Step1: Apply the triangle - inequality theorem

The triangle - inequality theorem states that for a triangle with side lengths \(a\), \(b\), and \(c\), \(|a - b|\lt c\lt a + b\). Here, \(a = 2\) and \(b=7\).
First, calculate \(|a - b|\):
\(|2 - 7|=| - 5| = 5\)
Second, calculate \(a + b\):
\(2+7 = 9\)

Answer:

C. \(5\lt x\lt9\)