jmc

We must find the distance between each pair of points by using the distance formula.

The distance between $(11,1)$ and $(2,3)$ is $\sqrt{(11-2{)}^2+(1-3{)}^2}=\sqrt{81+4}=\sqrt{85}$.

The distance between $(2,3)$ and $(3,7)$ is $\sqrt{(2-3{)}^2+(3-7{)}^2}=\sqrt{1+16}=\sqrt{17}$.

The distance between $(3,7)$ and $(11,1)$ is $\sqrt{(11-3{)}^2+(1-7{)}^2}=\sqrt{64+36}=\sqrt{100}=10$.

$10$ is larger than $\sqrt{85}$ and $\sqrt{17}$. Thus, the longest side of the triangle has length $\boxed{10}$.