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: Apply triangle - side inequality

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side, and the difference between the lengths of any two sides must be less than the length of the third side. Let the two given sides be \(a = 9\) and \(b=19\). Then \(|a - b|\lt x\lt a + b\).

Step2: Calculate the lower - bound

Calculate \(|9 - 19|=| - 10| = 10\). So \(x>10\).

Step3: Calculate the upper - bound

Calculate \(9 + 19=28\). So \(x<28\).

Answer:

A. \(10 < x < 28\)