Step 1: Recall the angle bisector theorem

          NOTE : An angle bisector of an angle of a triangle divides the opposite side

          in two segments that are proportional to the other two sides of the triangle.


Step 2: Set up a angle theorem  proportion in the given figure:

            NOTE: \frac{AB}{BC} = \frac{AD}{DC}

Step 3: Substitute all the known in the proportion

            EXAMPLE : \frac{5}{12} = \frac{3.5}{x}

Step 4: Solve for x

            Cross multiply.

                5x = 3.5 * 12

            Divide both sides by 5

                 x = \frac{42}{5}

                          x = 8.4 .

The value of x is 8.4