Pairs of Heron and right triangles with a common area and a common perimeter
Abhishek Juyal, Dustin Moody
A Heron triangle is one in which the side lengths and area are integers. An integral right triangle is an example of a Heron triangle. In this paper, we show that there are infinitely many pairs of integral right triangles and Heron triangles with a common area and common perimeter, continuing a line of similar results with other pairs of geometric shapes. This result is established using the theory of elliptic curves.
and Moody, D.
Pairs of Heron and right triangles with a common area and a common perimeter, Publicationes Mathematicae Debrecen, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=934575
(Accessed March 31, 2023)