Answer
$x = 6$
Work Step by Step
According to the triangle-angle-bisector theorem, when a ray bisects the angle of a triangle, the opposite side is divided into two segments that are proportional to the remaining two sides of the triangle.
Let's set up a proportion that compares the segments of the intersected side to the other two sides:
$\frac{5}{x} = \frac{10}{12}$
Use the cross product property to get rid of the fractions:
$10x = 60$
Divide each side of the equation by $10$ to solve for $x$:
$x = 6$
