Is there exists any general formula for shortest area of triangle with integeral sides where, perimeter is given?

Question

if the perimeter of triangle is given , then, how to find the shortest area of triangle with integral sides. Let, $P$ be perimeter and $s$ be semi-perimeter. we known,$s=P/2$

area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$

$\implies $ area of triangle = $\frac{\sqrt{p(p-2a)(p-2b)(p-2c)}}{4}$

this equation contains four variables $a,b,c,P$. by using relation $P=a+b+c$ we can make the equation contains three independent variables.

area of triangle = $\frac{\sqrt{(a+b+c)(b+c-a)(a+c-b)(a+b-c)}}{4}$

then how to I continue?