Heron triangle and rhombus pairs with a common area and a common perimeter

Abstract

By Fermat's method, we show that there are infinitely many Heron triangle and $\theta$-integral rhombus pairs with a common area and a common perimeter. Moreover, we prove that there does not exist any integral isosceles triangle and $\theta$-integral rhombus pairs with a common area and a common perimeter.

5 pages