The perimeter is the sum of all sides of the triangle. Since the triangle is not straight you must use the distance formula which is basically the Pythagorean theorem but used coordinates to solve for the sides.
I like to just use the Pythagorean theorem instead of coordinates. If you draw right triangles on the one in the picture with hypotenuse as the unknown sides.
3^2 + 5^2 = (AB)^2
9 + 25 = 34
sqrt(34) = AB
1^2 + 2^2 = (AC)^2
1 + 4 = 5
sqrt(5) = AC
3^2 + 4^2 = (BC)^2
9 + 16 = 25
sqrt(25) = 5 = BC
add up sides
perimeter = sqrt(34) + sqrt(5) + 5
