I am not going to do this problem for you, but I am going to explain how to do it. If you are in geometry, I am sure that you can do it, since it mostly is a matter of applying the Pythagorean Theorem.
First, sketch the triangle. I would do it on graph paper. The perimeter of a triangle is the sum of the lengths of its three sides, a simple addition problem once you have the lengths.
Getting the lengths is a little complicated but not bad. You are going to create three right triangles by dropping (or raising!) perpendiculars systematically from each vertex of the triangle. Once you get a perpendicular, you will attach it to another vertex to form a right angle. I would sketch these triangles using dashed lines to distinguish them from the sides of given triangle, RAT.
For instance, if I drop a perpendicular down from vertex T (5,5) along x=5, I only need to drop it to y=3, so that I can attach then perpendicular to vertex R (–2,3). I have created a right triangle for which I know the lengths of the legs; the hypotenuse of this triangle is the length of one side of given triangle RAT, the side RT. By the way, the length of the sides of the created triangle, which you are going to plug into the Pythagorean Theorem equation are 2 (= 5 – 3) and 7 (= 5 – [–2]).
I'll go ahead and show you the equation: 22 + 72 = h2.
4 + 49 = h2
53 = h2√
√53 = h
One side of RAT has a length of √53. It's the "upper side" of the triangle, so to speak.
Good luck with the rest. I have no doubt that if you carefully follow my instructions, you can learn something and solve the perimeter problem.
