Question

the side lengths of a triangle are 8, 14, and x units.
(the figure above gives only one possible configuration for the triangle.)
determine the possible values of x.
write your answer as an inequality.
use x only once in your inequality.

Explanation:

Step1: Apply the triangle inequality theorem (difference of two sides)

The difference of two sides of a triangle is less than the third side. So \(14 - 8

Step2: Apply the triangle inequality theorem (sum of two sides)

The sum of two sides of a triangle is greater than the third side. So \(x<14 + 8\), which simplifies to \(x<22\).

Answer:

\(6 < x < 22\)