An application of Poincare inequality [solved]

Question

I am woking on Evans PDE problem 5.10. #15: Fix $\alpha>0$ and let $U=B^0(0,1)\subset \mathbb{R}^n$. Show there exists a constant $C$ depending only on $n$ and $\alpha$ such that $$ \int_U u^2 dx \le C\int_U|Du|^2 dx, $$ provided that $u\in W^{1,1}(U)$ satisfies $$ |\{x\in U\ |\ u(x)=0\}|>\alpha. $$ I would appreciate your helping me with this problem.