# Relation Between Side Lengths And Median

Geometry Level 3

In $$\triangle{ABC}$$, $$D$$ is the midpoint of $$BC$$. Given that $$AB=3$$cm, $$AC=5$$cm and $$BC=7$$cm, $$AD$$ can be expressed in the form $$\frac{\sqrt{m}}{n}$$, where $$m$$ and $$n$$ are positive integers and $$m$$ is not divisible by the square of any prime. Find the value of $$m+n$$.

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