29.5k views
1 vote
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.

User Hyounis
by
8.0k points

2 Answers

3 votes

Answer:

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 :)

User Jonasnas
by
8.3k points
3 votes
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.


User Leu
by
8.1k points

No related questions found