Question

Hey there! I’m having a bit of trouble with this one, I think I’ve been looking at this for too long. If you could give me an explanation, I would be appreciate it! Thanks in advance! This is a practice test.

Answer 1

AD = 42-x

The bisector of an angle of a triangle divides the opposite side into segments that are proportional to the adjacent sides  ⇒
AB/BC = AD/DC
36/27 = (42-x)/x
36x = 27(42-x)
36x = 1134 - 27x
36x + 27x = 1134
63x = 1134
x = 1134/63
x = 18