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Integral Isosceles Triangle-Parallelogram and Heron triangle-Rhombus Pairs with a Common Area and Common Perimeter



Pradeep Das, Abhishek Juyal, Dustin Moody


In this paper we show that there are in nitely many pairs of integer isosceles triangles and integer parallelograms with a common (integral) area and common perimeter. We also show that there are in nitely 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.
Journal of Number Theory


Elliptic Curve, Isosceles Triangle, Heron Triangle, Rhombus, Parallelogram
Created June 6, 2017, Updated November 10, 2018