Triângulos com lados inteiros e racionais : uma maneira de trabalhar no ensino fundamental e médio.

Abstract

In this work we begin by studying triangles with integer sides whose area and perimeter are related. We also show that starting from any given rational-sided, right triangle, for example the (3,4,5)-triangle with area 6, we use Euclidean geometry to show that there are infinitely many other rational-sided, right triangles of the same area. We show further that the set of all such triangles of a given area is finitely generated under our geometric construction. Such areas are known as “congruent numbers” and have a rich history.