Given the following figure, find the numerical values of and .
If a line segment is drawn parallel to one side of a triangle and intersects the other two sides, then it divides the other two sides into segments whose lengths are proportional. This means that . Since , it must be true that . First, use this fact to solve for as follows:
Now use the fact that to solve for .
Thus, the value of is 8, and the value of is 13.