By applying the angle bisector theorem to triangle ABC, the length of AB is: A. 32.
In Mathematics and Euclidean Geometry, an angle bisector is a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal and congruent angles.
According to the angle bisector theorem, a ray divides the opposite side of a triangle into segments that are proportional to the other two (2) sides when it bisects an angle of the triangle.
By applying the angle bisector theorem to triangle ABC, we have the following proportional sides;
AC/AB = CD/DB
40/AB = 10/8
10AB = 320
AB = 320/10
AB = 32 units.