Because in the following inequality $$S=\sqrt{p(p-a)(p-b)(p-c)}\le \sqrt{p\Big(\frac{(p-a)+(p-b)+(p-c)}{3}\Big)^3}=\frac{p^2}{\sqrt{27}}$$ the equality holds if and only if $(p-a)=(p-b)=(p-c)$, i.e. $a=b=c$.