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

This is not my work but i hope this can help you with your problem
https://answers.yahoo.com/question/index?qid=20120518194118AAhi738

Answer 2

Answer:

Option D -8.3 cm, 5.8 cm

Step-by-step explanation:

Given : 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.

To find : The longest and shortest possible lengths of the third side of the triangle?

Solution :

First we create the image of the question,

Refer the attached figure below.

Let a triangle ABC , where angle A has a bisector AD such that D is on the side BC.

The theorem is stated for angle bisector is

"Each angle bisector of a triangle divides the opposite side into segments proportional in length to the adjacent sides".

So, according to question,

Let BD=6 cm, DC=5 cm, AB=6.9 cm

and we have to find AC.

Applying the theorem,

$\frac{BD}{DC}=\frac{AB}{AC}$

$\frac{6}{5}=\frac{6.9}{AC}$

$AC=\frac{6.9\times 5}{6}$

$AC=\frac{34.5}{6}$

$AC=5.75$

$AC=5.8 cm$

If we let AC=6.9 cm, find AB

Then,

$\frac{BD}{DC}=\frac{AB}{AC}$

$\frac{6}{5}=\frac{AB}{6.9}$

$AB=\frac{6.9\times 6}{5}$

$AB=\frac{41.4}{6}$

$AB=8.28$

$AB=8.3 cm$

Therefore, The shortest possible length is 5.8 cm and longest possible is 8.3 cm.

Hence, Option D is correct.