x=9 i.e. option B is the answer.
Step-by-step explanation:
Given that in triangle ABC, sides AB and BC are 36 and 28 units.
BD is angle bisector of angle B meeting AC at point D
Also AC = 16 cm.
We know that by angle bisector theorem,
AB/AC = BD/DC
Or x/DC = 36/28
By compendo and dividendo principle, we rewrite as
Or x/x+DC = 36/(28+36)
x/16 = 36/64
x = 36(16)/64 = 9 units.