Question

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.

Answer 1

The answer is D) 8.3 cm, 5.8 cm

Explanation:

The answers for the U3L5: Proportions in Triangles Quiz in Connexus are:

1. A) ∆UVW ~ ∆UWT ~ ∆ WVT

2. A)
`a=(9)/(2) , b=(15)/(2)`

3. A) 5

4. A)
`46(2)/(3)\:yards`

5. D) 8.3 cm, 5.8 cm

I just took the quiz and got 100%

hope this helps :)

Answer 2

Based in the information given in the problem, you must apply the The Angle Bisector Theorem. Let's call the triangle: "ABC"; the internal bisector of the angle that divides its opposite side: "AP"; and "x": the longest and shortest possible lengths of the third side of the triangle.

If BP= 6 cm and CP= 5 cm, we have:

BP/CP = AB/AC

We don't know if second side of the triangle (6.9 centimeters long) is AB or AC, so:

1. If AB = 6.9 cm and AC = x:
6/5 = 6.9/x
x = (5x6.9)/6
x = 5.80 cm

2. If AC= 6.9 cm and AB= x:
6/5 = x/6.9
x = 6.9x6/5
x = 8.30 cm

Then, the answer is:
The longest possible length of the third side of the triangle is 8.30 cm and the and shortest length of it is 5.80 cm.