SOLUTION: I have a triangle. A bisector divides one of its angles into two parts. The side divided into two parts - one part is x and total of two parts is 8. One of the other two sides is 5

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Question 1114764: I have a triangle. A bisector divides one of its angles into two parts. The side divided into two parts - one part is x and total of two parts is 8. One of the other two sides is 5 and the other is 7. find the x.
If i couldn’t explain my problem very well you can type angle bisector theorem practice in google and click what came out the first. I am stuck in the 4th problem.
Thanks in advance.
Found 2 solutions by rothauserc, ikleyn:
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
the angle bisector divides the side of the triangle, proportionally
:
5/x = 7/(8-x)
:
cross multiply the fractions
:
5(8-x) = 7x
:
40 -5x = 7x
:
12x = 40
:
x = 40/12 = 10/3
:
*********************************
answer is 3 and 1/3
*********************************
:
Answer by ikleyn(52817)   (Show Source): You can put this solution on YOUR website!
.
For your info: 

    There is a Theorem in Elementary Geometry:

      In any triangle, an angle bisector divides the opposite side in the ratio, equal to the ratio of two other sides of the triangle.


See the lesson
    - On what segments the angle bisector divides the side of a triangle
in this site.

--------------------
Also,  you have this free of charge online textbook on Geometry
    GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.

The referred lesson is the part of this online textbook under the topic  "Properties of triangles".


Save the link to this online textbook together with its description

Free of charge online textbook in GEOMETRY
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson

to your archive and use it when it is needed.


It is the best available source (textbook) in Geometry which I know . . .



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