Answer:
D. 15
Step-by-step explanation:
Let the missing length be represented as x.
Thus:
(24 - x)/12 = x/20 => angle bisector theorem
Cross multiply
20(24 - x) = x(12)
480 - 20x = 12x
480 - 20x + 20x = 12x + 20x
480 = 32x
480/32 = 32x/32
15 = x
Missing length = x = 15
ANSWER

EXPLANATION
First equation:

Second equation:

Let us equate the two equations and solve for x.
This implies that;

Group similar terms to obtain:

Simplify:

Divide both sides by 3

Put x=-2 into any of the equations.
I will put x=-2 into the first equation:

This implies that,

<em>so</em><em> </em><em>the</em><em> </em><em>answer</em><em> </em><em>is</em><em> </em><em>of</em><em> </em><em>option</em><em> </em><em>C</em><em>.</em><em>.</em><em>.</em><em>.</em>