Some Special Analysation on a Pythagorean Triangle which Satisfies $\alpha\left((Hypotonuse\times Perimeter)-4\left(Area\right)\right)=$ $\lambda^{2}\left(Perimeter\right)$ for Some Particular Different Values of $\alpha$

Abstract

We obtain non-trivial integer solutions for the sides of the Pythagorean triangle, for some particular values of $\alpha$ which satisfies $\left(\alpha ((Hypotonuse\times Perimeter)-4\left(Area\right))\right)=\lambda^{2}\left(Perimeter\right)$. A few interesting relations between the sides of the Pythagorean triangle are presented.