Pairs of equiperimeter and equiareal triangles whose sides are perfect squares

TL;DR

This paper investigates pairs of triangles with sides as perfect squares that share the same perimeter and area, discovering specific pairs and proving the existence of infinitely many such pairs.

Contribution

It identifies two explicit pairs of triangles with perfect square sides sharing perimeter and area, and proves infinitely many such pairs exist.

Findings

Found two specific pairs of triangles with perfect square sides sharing perimeter and area.

Proved the existence of infinitely many such pairs.

Established conditions for pairs of triangles with perfect square sides to have common perimeter and area.

Abstract

In this paper we consider the problem of finding pairs of triangles whose sides are perfect squares of integers, and which have a common perimeter and common area. We find two such pairs of triangles, and prove that there exist infinitely many pairs of triangles with the specified properties.