A triangle has corners at points A, B, and C. Side AB has a length of #48 #. The distance between the intersection of point A's angle bisector with side BC and point B is #24 #. If side AC has a length of #27 #, what is the length of side BC?

1 Answer
Sep 18, 2017

#37 1/2" units"#

Explanation:

#"let D be the point of intersection between the angle"#
#"bisector and the side 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)|))#

#rArr48/27=24/(DC)larrcolor(blue)" cross-multiply"#

#rArrDCxx48=24xx27#

#rArrDC=(24xx27)/48=27/2=13 1/2#

#BC=BD+DC=24+13 1/2=37 1/2" units"#