Question

A triangle has corners at points A, B, and C. Side AB has a length of `21`. The distance between the intersection of point A's angle bisector with side BC and point B is `7`. If side AC has a length of `24`, what is the length of side BC?

Answer 1

15 units

Explanation:

Firstly , let the point where the angle bisector intersects with side BC be D.

Then by the `color(blue)" Angle bisector theorem "`

`( BD)/(DC) = (AB)/(AC) ", DC is required to be found "`

substitute in the appropriate values into the ratios to obtain:

`7/(DC) = 21/24 rArr 21DC = 7xx24rArr DC = (7xx24)/21 = 8`

now BC = BD + DC = 7 + 8 = 15 units