Perpendicular Medians

Geometry Level 4

In the triangle $$ABC$$, point $$D$$ is located on edge $$AC$$ and point $$E$$ is located on edge $$AB$$. $$BD$$ and $$CE$$ are the medians, and intersect at a right angle at $$O$$. Given $$BD = 8$$ and $$CE = 12$$, if $$x$$ is the area of triangle $$ABC$$, find the value of $$x+8$$.

×