# 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 \(m+n\).