Question

An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 4 cm long. A second side of the triangle is 7.4 cm long. Find the longest and shortest possible lengths of the third side of the triangle. Round answers to the nearest tenth of a centimeter. Question 3 options: 11.1 cm, 4.9 cm 44.4 cm, 3.2 cm 44.4 cm, 11.1 cm 24 cm, 4.9 cm

Answer 1

11.1 cm, 4.9 cm

Answer 2

You can solve this problem by applying the Angle Bisector Theorem. Let's call the lenghts we want to calculate: "x":

7.4/x=6/4

When we clear "x", we obtain:

6x=(7.4)(4)
x=(7.4)(4)/6
x=4.9 cm (This is the shortest possible length of the third side of the triangle)

Let's find the longest possible length:

4/6=7.4/x

When we clear the "x", we have:

4x=(7.4)(6)
x=(7.4)(6)/4
x=11.1 cm (This is the longest possible length of the third side of the triangle)