Question

two sides of a triangle have the following measures. find the range of possible measures for the third side.
2, 19

Explanation:

Step1: Apply triangle inequality theorem (difference)

Let the two given sides be \(a = 2\) and \(b=19\). The difference of the two sides is \(|b - a|=|19 - 2|=17\).

Step2: Apply triangle inequality theorem (sum)

The sum of the two sides is \(a + b=2+19 = 21\).

Answer:

The range of possible measures for the third side \(x\) is \(17\lt x\lt21\).