Question

in △cab, if the measure of $overline{ab}$ is 8 units and the measure of segment $overline{ac}$ is 5 units, which of the following could be the measure of segment $overline{cb}$? 12 units 13 units 14 units 15 units

Explanation:

Step1: Apply triangle - inequality theorem

The triangle - inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), the following three inequalities must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\). In \(\triangle CAB\), let \(a = 5\) (length of \(\overline{AC}\)), \(b\) be the length of \(\overline{CB}\), and \(c = 8\) (length of \(\overline{AB}\)). Then \(|a - c|

Step2: Calculate the range of \(b\)

Substitute \(a = 5\) and \(c = 8\) into the inequality \(|a - c|

Answer:

12 units