# Area without knowing the side lengths

Geometry Level 3

In a triangle $$ABC$$, the medians $$AD$$ and $$BE$$ are perpendicular to each other and their lengths are $$AD=m$$ and $$BE=n$$. If the area of triangle $$ABC$$ is of the form
$$\dfrac {amn}b$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

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