Question

An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 5cm long. A second side of the triangle is 6.9cm long. Find the longest and shortest possible lengths of the third side of the triangle. Round answers to the nearest tenth of centimeter.

Answer 1

Segments either side of an angle bisector are proportional.

The longest the third side (x) could be is
6/5 = x/6.9
x = 6/5*6.9 = 8.28

The shortest the third side could be is
5/6 = x/6.9
x = 5/6*6.9 = 5.75

The longest and shortest possible lengths for the third side are ...
8.3 cm and 5.8 cm.