A triangle has corners at points A, B, and C. Side AB has a length of #21 #. The distance between the intersection of point A's angle bisector with side BC and point B is #5 #. If side AC has a length of #18 #, what is the length of side BC?

1 Answer
Jim G.
Feb 11, 2017

#BC=9 2/7" units"#

Explanation:

Let D be the point on BC where the angle bisector, intersects with BC

Then BC = BD+ CD

We know that BD = 5 and have to find CD

Using the #color(blue)"Angle bisector theorem"# on this triangle.

#color(red)(bar(ul(|color(white)(2/2)color(black)((BD)/(CD)=(AB)/(AC))color(white)(2/2)|)))#

Substituting known values into this equation.

#rArr5/(CD)=21/18#

#color(blue)"cross multiply"#

#rArr21CD=5xx18#

#rArrCD=90/21=30/7=4 2/7#

#rArrBC=5+4 2/7=9 2/7#

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