Let the vertices of the triangle be given by (0, 0), (a, b), and (c, d).
We divide the work into cases, looking for a lattice triangle with sides of 15, 34, or 35, or proving that no such lattice triangle exists.
Case 1: the side length of 15 touches the origin.
Case 2: the side length of 15 does not touch the origin.
To analyze case 1, first assume that the side of length 15 lies between the origin and (a, b). Also, without loss of generality, assume that a and ...
Constructing a lattice from a Heron Triangle is examined. Pythagorean triangles are determined.