Question

An angle bisector of a triangle divides the opposite side of the triangle into segments2 cm and 5cm long. The second side of the triangle is 7.5 cm long. Find all possible lengths for the third side of the triangle.

Answer 1

• 3 cm or 18.75 cm

Explanation:

Let the third side is x.

According to Triangle-angle-bisector theorem, we have the possible ratios:

• x/7.5 = 2/5

or

• x / 7.5 = 5/2

Solve for x in each case:

1)

• x = 7.5*2/5 = 3 cm

2)

• x = 7.5*5/2 = 18.75 cm