Question

5. An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 5 cm long. A second side of the triangle is 6.9 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. (1 point)

A. 41.4 cm, 8.3 cm
B. 30 cm, 5.8 cm
C. 41.4 cm, 4.3 cm
D. 8.3 cm, 5.8 cm

Answer 1

You have to set up 2 proportions.

If the 6.9 goes with the 5 then the proportion will look like this.
6.9/5 = x/6 Cross multiply
6 * 6.9 = 5x
41.4 / 5 = x
x = 8.28 or 8.3

If on the other hand the 6.9 goes with the 6 then the second proportion is
6.9/6 = x/5
6.9 * 5 = 6X
34.5 / 6 = x
x = 5.75

Answer: D <<<<<<<<======