Question

A triangle has corners at points A, B, and C. Side AB has a length of `32`. The distance between the intersection of point A's angle bisector with side BC and point B is `16`. If side AC has a length of `28`, what is the length of side BC?

Answer 1

30

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)`

Require to find DC.

Substitute the appropriate values into the ratio to obtain.

`(16)/(DC) = 32/28`

now cross-multiply : `32xxDC = 28xx16`

To obtain DC , divide both sides by 32

`( cancel(32) DC)/cancel(32) = (28xx16)/32`

`rArr DC = 14`

Now , BC = BD + DC = 16 + 14 = 30