Question

A triangle has corners at points A, B, and C. Side AB has a length of `6`. The distance between the intersection of point A's angle bisector with side BC and point B is `4`. If side AC has a length of `8`, what is the length of side BC?

Answer 1

`28/3=9 1/3" units"`

Explanation:

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

`rArrBC=BD+DC`

`BD=4" require to find "DC`

`"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)|)))`

`rArr6/8=4/(DC)larrcolor(blue)" cross-multiply"`

`rArr6DC=8xx4`

`rArrDC=(8xx4)/6=32/6=16/3`

`rArrBC=4+16/3=28/3=9 1/3" units"`