Question

An angle bisector of a triangle divides the opposite side of the triangle into segments 1.5 cm and 1 cm long. A second side of the triangle is 2.6 cm long. Find all possible lengths of the third side of the triangle. Round answers to the nearest tenth of a centimeter. (Hint: Draw a picture of the triangle, label one side with 2.6 cm, and solve for the other side. Then, move the 2.6 cm to the other side and solve.)

Answer 1

By the angle bisector theorem, one of the lengths of the third side of the triangle is given by:
1.5 / 1 = x / 2.6
x = 1.5 x 2.6 = 3.9
One of the possible length of the third side is 3.9 cm

The other possible length is given by 1 / 1.5 = x / 2.6
1.5x = 2.6
x = 2.6/1.5 = 1.7
The other possible length of the third side is 1.7 cm.