Integral Isosceles Triangle-Parallelogram and Heron triangle-Rhombus Pairs with a Common Area and Common Perimeter
Das, P.; Juyal, A.; Moody, D.
Journal of Number Theory 180: 208-218
ISSN/ISBN: 0022-314X PMID: 28966397 DOI: 10.1016/j.jnt.2017.04.009
In this paper we show that there are infinitely many pairs of integer isosceles triangles and integer parallelograms with a common (integral) area and common perimeter. We also show that there are infinitely many Heron triangles and integer rhombuses with common area and common perimeter. As a corollary, we show there does not exist any Heron triangle and integer square which have a common area and common perimeter.