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
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"#