Square $$AIME$$ has sides of length $$10$$ units. Isosceles triangle $$GEM$$ has base $$EM$$, and the area common to triangle $$GEM$$ and square $$AIME$$ is $$80$$ square units. Find the length of the altitude to $$EM$$ in $$\triangle GEM$$.

(第二十六届AIME1 2008 第2题)