Question

Triangle \(ABC\) has side lengths \(AB=c=6, AC=b=5,\) and \(BC=a=4.\) A point \(P\) in the interior of \(\triangle ABC\) is a distance \(l\) from \(BC\), a distance \(m\) from \(AC\), and a distance \(n\) from \(AB\). If \(l^2 + m^2 + n^2 = 225/44,\) then find \(l^2\).