Chapter 5.3, Problem 45HP

To determine

To find: The possible measure for $\overline{AB}$ in the triangle $\Delta ABC$ and explain the reasoning.

Answer to Problem 45HP

The required diagram is shown in Figure 1 as the possible measure for $\overline{AB}$ must be more than 6 by angle-side relationship.

Explanation of Solution

Consider a triangle that has one side longer than the other side only when the angle that is only that is opposite to the longer side greater measure than the angel opposite to the shorter side.

The objective is to obtain the triangle that has $\overline{AB}$ as possible measure.

The required diagram is shown in Figure 1

  

Figure 1

Apply angle-side relationship theorem in the above triangle. This shows that $AB>AC$ . Thus, the possible measure for $\overline{AB}$ must be more than 6.