Question

Can someone please help me out with this geometry problem? I've been stuck on it for almost an hour.

Answer 1

The answer is
`x = 16`

Explanation:

Solution:

Let we first name the Triangle as Δ ABC and ray BD as a bisector of ∠B

as shown in the figure below.

As ray BD is the bisector of angle B so, by Angle bisector theorem property we have

`(AB)/(BC) = (AD)/(DC)\\`

∴
`(x)/(12) =(x-4)/(9)`

∴
`(x)/(4) = (x-4)/(3)`

∴
`3x = 4x -16`

∴
`x = 16` final answer