jmc

Wanda is trying to locate the Fermat point $P$ of $△ABC$, where $A$ is at the origin, $B$ is at $(8,-1)$, and $C$ is at $(5,4)$ (the Fermat point is the point such that the sum of its distances from the vertices of a triangle is minimized). She guesses that the point is at $P=(4,2)$, and computes the sum of the distances from $P$ to the vertices of $△ABC$. If she obtains $m+n\sqrt{5}$, where $m$ and $n$ are integers, what is $m+n$?