A triangle has corners at points A, B, and C. Side AB has a length of #18 #. The distance between the intersection of point A's angle bisector with side BC and point B is #3 #. If side AC has a length of #24 #, what is the length of side BC?

1 Answer

#BC=7#

Explanation:

#"let D be the point where the angle bisector meets 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)|)))#
Require to find DC.

#rArr18/24=3/(DC)#

#color(blue)"cross-multiplying"# gives.

#18DC=3xx24#

#rArrDC=(3xx24)/18=4#

#BC=BD+DC=3+4=7#