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
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#