Question

two sides of a triangle measure 9 and 19. which inequality shows all the possible lengths of the third side, x? a 10 < x < 28 b 9 < x < 10 c 19 < x < 28 d 9 < x < 19

Explanation:

Step1: Recall triangle - side rule

The length of the third side \(x\) of a triangle with two side - lengths \(a\) and \(b\) satisfies the inequality \(|a - b|\lt x\lt a + b\). Here \(a = 9\) and \(b = 19\).

Step2: Calculate the lower - bound

First, find \(|a - b|\): \(|9 - 19|=| - 10| = 10\).

Step3: Calculate the upper - bound

Then, find \(a + b\): \(9+19 = 28\).
So, \(10\lt x\lt28\).

Answer:

A. \(10\lt x\lt28\)