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soldi70 [24.7K]
3 years ago
13

an angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 5cm 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.
Mathematics
2 answers:
cricket20 [7]3 years ago
5 0

Answer:

Proportions In Triangles Quiz Connexus

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

These are correct i got a 100% Have A Blessed Day

Step-by-step explanation:

rodikova [14]3 years ago
4 0
There is a not so well-known theorem that solves this problem.

The theorem is stated as follows:
"Each angle bisector of a triangle divides the opposite side into segments proportional in length to the adjacent sides"  (Coxeter & Greitzer)

This means that for a triangle ABC, where angle A has a bisector AD such that D is on the side BC, then 
BD/DC=AB/AC

Here either
BD/DC=6/5=AB/AC, where  AB=6.9,  
then we solve for  AC=AB*5/6=5.75,

or

BD/DC=6/5=AB/AC, where  AC=6.9,  
then we solve for AB=AC*6/5=8.28

Hence, the longest and shortest possible lengths of the third side are
8.28 and 5.75 units respectively.

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The solution to the system of equations is x = 8, y = 4.

<h3>How to write the system of equations?</h3>

First, let's define our variables as x and y.

"the sum of two numbers is twelve" is written as:

x + y = 12

"two times the first number minus three times the second number is four" is written as:

2x - 3y = 4

Then the system of equations is:

x + y  = 12

2x - 3y = 4

<h3>How to solve it?</h3>

First, we isolate one of the variables in one equation, I will isolate x on the first one to get:

x = 12 - y

Now we replace this on the other equation, so we get:

2*(12 - y) - 3y = 4

Now we can solve this for y.

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