A triangle has corners at points A, B, and C. Side AB has a length of #15 #. The distance between the intersection of point A's angle bisector with side BC and point B is #8 #. If side AC has a length of #15 #, what is the length of side BC?
2 Answers
Dec 21, 2017
Length of side
Explanation:
Let the point where the angle bisector intersects with
side BC be D
#"using the "color(blue)"angle bisector theorem"#
It’s an isosceles triangle with sides AB & AC equal.
Hence BD = DC & BC = BD + DC = 2*BD
Dec 21, 2017
Explanation:
#"let the point where the angle bisector intersects BC be D"#
#"using the "color(blue)"angle-bisector theorem"" then"#
#color(red)(bar(ul(|color(white)(2/2)color(black)((AB)/(AC)=(BD)/(DC))color(white)(2/2)|)))#
#rArr15/15=8/(DC)larrcolor(blue)"cross-multiply"#
#15xxDC=8xx15#
#rArrDC=(8xx15)/15=8#
#rArrBC=BD+DC=8+8=16#