Given a $\triangle ABC$ with the edges $a,b$ and $c$ and the area $S$: (a) Prove that there exists $\triangle A_1B_1C_1$ with the sides $\sqrt a,\sqrt b$ and $\sqrt c$. (b) If $S_1$ is the area of $\triangle A_1B_1C_1$, prove that $S_1^2\ge\frac{S\sqrt3}4$.