A triangle has corners at points A, B, and C. Side AB has a length of #10 #. The distance between the intersection of point A's angle bisector with side BC and point B is #4 #. If side AC has a length of #8 #, what is the length of side BC?

1 Answer
Jim G.
Oct 31, 2017

#BC=7 1/5" units"#

Explanation:

#"let D be the point on BC where the angle bisector"#
#"intersects BC"#

#"using the "color(blue)"angle bisector theorem"#

#color(red)(bar(ul(|color(white)(2/2)color(black)((AB)/(AC)=(BD)/(DC))color(white)(2/2)|)))larr" find DC"#

#rArr10/8=4/(DC)#

#rArrDC=(4xx8)/10larrcolor(blue)"cross-multiplying"#

#rArrDC=32/10=3 1/5#

#rArrBC=BD+DC=4+3 1/5=7 1/5" units"#

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