This paper is concerned with the problem of finding two or more rational triangles with the same perimeter and the same area. As the problem of finding two isosceles rational triangles with the same perimeter and same area has already been solved, in this paper we obtain several parametric solutions to the problem of finding a pair of rational triangles with the same area and perimeter when at least one of the triangles is scalene. We also show that, with certain exceptions, given an arbitrary scalene rational triangle, a second scalene rational triangle with the same perimeter and same area may be constructed, and by repeated application of this process, we may obtain an arbitrarily large number of scalene rational triangles with the same perimeter and same area.