Question

question 8 (multiple choice worth 1 points) (02.04r mc) in \\( \triangle c a b \\), if the measure of \\( \overline{a b} \\) is 8 units and the measure of segment \\( \overline{a c} \\) is 5 units, which of the following could be the measure of segment \\( \overline{c b} \\)? 12 units 13 units 14 units 15 units

Explanation:

Step1: Use triangle inequality theorem

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Let \(AC = 5\), \(AB=8\), and \(CB=x\). Then \(AC + AB>CB\), \(AC + CB>AB\), and \(AB + CB>AC\). From \(AC + AB>CB\), we have \(5 + 8>x\) (i.e., \(x<13\)). From \(AC+CB > AB\), \(5+x>8\) (i.e., \(x > 3\)). From \(AB + CB>AC\), \(8 + x>5\) (always true for positive \(x\)).

Answer:

12 units