Arithmetic problems of plane geometry | Types of triangles | Articles containing proofs
Heronian triangle
In geometry, a Heronian triangle (or Heron triangle) is a triangle whose side lengths a, b, and c and area A are all integers. Heronian triangles are named after Heron of Alexandria, based on their relation to Heron's formula. Heron's formula implies that the Heronian triangles are exactly the positive integer solutions of the Diophantine equation that is, the side lengths and area of any Heronian triangle satisfy the equation, and any positive integer solution of the equation describes a Heronian triangle. If the three side lengths are coprime, the Heronian triangle is called primitive. Triangles whose side lengths and areas are all rational numbers (positive rational solutions of the above equation) are sometimes also called Heronian triangles; in this article, these more general triangles will be called rational Heronian triangles. Every (integral) Heronian triangle is a rational Heronian triangle. Conversely, every rational Heronian triangle is similar to exactly one primitive Heronian triangle. (Wikipedia).
