Question

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?

Answer 1

`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`