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 t
he 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.)
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.