  Many authors studied the problem that rational triangle pairs
(triangle-parallelogram pairs) with the same area and the same perimeter. They
investigated this problem by solving the rational solutions of the
corresponding Diophantine equations. In this paper, we give a unified
description of this problem by using the affine transformation in a rectangular
coordinate system. According to the fact that two triangles with the same area
and the same perimeter determine an affine transformation, this problem can be
reduced to solving a specific Diophantine system. Moreover, we will give some
rational solutions to this Diophantine system.
