Label the vertices A:(2,9);B:(3,0) and C(1,3).

To find the perimeter of the triangle we find the lengths of each of the sides. To find the length, use the distance formula: between points `(x_1,y_1),(x_2,y_2) ` the distance `d ` is given by `d=sqrt((x_2-x_1)^2+(y_2-y_1)^2) ` . Note that the distance formula is just the Pythagorean theorem.

`AB=sqrt(1^2+9^2)=sqrt(82) `

`BC=sqrt(2^2+3^2)=sqrt(13) `

`AC=sqrt(1^2+6^2)=sqrt(37) `

Then the perimeter is ` p=sqrt(82)+sqrt(13)+sqrt(37) `