Question

A triangle has corners at points A, B, and C. Side AB has a length of `12`. 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 `24`, what is the length of side BC?

Answer 1

`24" units"`

Explanation:

`"let the point where the angle bisector intersects with"`
`"side BC be D"`

`"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)|)))`

`rArr12/24=8/(DC)larrcolor(blue)"cross-multiplying gives"`

`12xxDC=8xx24`

`rArrDC=(8xx24)/12=16`

`rArrBC=BD+DC=8+16=24" units"`