# Solving for a Length given the Medians

Geometry Level pending

Consider a $$\triangle ABC$$ with midpoints $$D$$, $$E$$, and $$F$$ on sides $$AB$$, $$BC$$, and $$CA$$ respectively. The lengths of segments $$AE$$, $$BF$$, and $$CD$$ are $$4$$, $$\sqrt{10}$$, and $$\sqrt{3}$$ respectively. The length of segment $$EF$$ can be written in the form $$\dfrac{j}{k}$$ where $$j$$ and $$k$$ are coprime positive integers. Calculate $$j + k$$.

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