Question

A triangle has corners at points A, B, and C. Side AB has a length of `48`. The distance between the intersection of point A's angle bisector with side BC and point B is `24`. If side AC has a length of `27`, what is the length of side BC?

Answer 1

`37 1/2" units"`

Explanation:

`"let D be the point of intersection between the angle"`
`"bisector and the side 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)|))`

`rArr48/27=24/(DC)larrcolor(blue)" cross-multiply"`

`rArrDCxx48=24xx27`

`rArrDC=(24xx27)/48=27/2=13 1/2`

`BC=BD+DC=24+13 1/2=37 1/2" units"`