A triangle has corners at points A, B, and C. Side AB has a length of #6 #. 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
Aug 27, 2017

#28/3=9 1/3" units"#

Explanation:

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

#rArrBC=BD+DC#

#BD=4" require to find "DC#

#"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)|)))#

#rArr6/8=4/(DC)larrcolor(blue)" cross-multiply"#

#rArr6DC=8xx4#

#rArrDC=(8xx4)/6=32/6=16/3#

#rArrBC=4+16/3=28/3=9 1/3" units"#