A triangle has corners at points A, B, and C. Side AB has a length of #7 #. 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 #14 #, what is the length of side BC?

1 Answer
Jul 7, 2017

#BC=12#

Explanation:

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

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

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

#rArr14/7=(CD)/4larrcolor(blue)" cross-multiply"#

#rArr7CD=4xx14#

#rArrCD=(4xx14)/7=8#

#rArrBC=CD+BD=8+4=12#