  A perfect triangle is a triangle with rational sides, medians, and area. In
this article, we use a similar strategy due to Pocklington to show that if
$\Delta$ is a perfect triangle, then it cannot be an isosceles triangle. It
gives a partial answer to a question of Richard Guy, who asked whether any
perfect triangles exist. No example has been found to date. It is widely
believed that such a triangle does not exist.
