Allan J. Macleod, On integer relations between the area and
perimeter of Heron triangles,
Forum Geometricorum, 9 (2009) 41--46.
Abstract: We discuss the relationship P^2 = nA for a triangle with
integer sides, with perimeter P and area A, where n is an integer. We show
that the problem reduces to finding rational points of infinite order in
a family of elliptic curves. The geometry of the curves plays a crucial role
in finding real triangles.