SOLUTION: In triangle ABC, AX bisects angle BAC. Find the value of x. Image of triangle: https://i.imgur.com/nIVWbbx.png

Algebra ->  Triangles -> SOLUTION: In triangle ABC, AX bisects angle BAC. Find the value of x. Image of triangle: https://i.imgur.com/nIVWbbx.png       Log On


   

Question 1111349: In triangle ABC, AX bisects angle BAC. Find the value of x.
Image of triangle: https://i.imgur.com/nIVWbbx.png
Answer by ikleyn(52909) About Me  (Show Source):
You can put this solution on YOUR website!
.
Use the Theorem: 

    In a triangle,  the angle bisector divides the side to which it is drawn, in two segments proportional 
    to the ratio of two other sides of a triangle.

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

When you use it, you get the proportion

    %284x-5%29%2F%282x%29 = 6%2F8,   or

    %284x-5%29%2F%282x%29 = 3%2F4.


Cross multiply

    4*(4x-5) = 3*(2x),

    16x - 20 = 6x,

    16x - 6x = 20  ====>  10x = 20  ====>  x = 20%2F10 = 2.


Answer.   x = 2.

-----------------------
Solved.

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.