jmc

We use the distance formula on each pair of points. From $A$ to $B$: $\sqrt{(1-1{)}^2+(8-2{)}^2}=6$ From $B$ to $C$: $\sqrt{(5-1{)}^2+(5-8{)}^2}=\sqrt{16+9}=\sqrt{25}=5$ From $C$ to $A$: $\sqrt{(5-1{)}^2+(5-2{)}^2}=\sqrt{16+9}=\sqrt{25}=5$ Adding the three side lengths of the triangle together, we get $6+5+5=\boxed{16}$.