How do you find the base of this triangle? (picture should be able to be seen)

The idea being, when you run a perpendicular line to the base, from the right-angle in a right-triangle, like in this case, what you end up with is, three similar triangles, a Large triangle containing the two smaller ones, a Medium triangle and a Small one, check the picture below.

since all three are similar, we can use the proportions on the corresponding sides, as you see in the picture, the base of the triangle then will just be x + y.