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 inequality theorem (difference)

The difference of two sides of a triangle is less than the third side. So \(19 - 9

Step2: Apply triangle inequality theorem (sum)

The sum of two sides of a triangle is greater than the third side. So \(x<19 + 9\), which simplifies to \(x < 28\).

Answer:

A. \(10 < x < 28\)