We prove that any extended formulation that approximates the matching polytope on n-vertex graphs up to a factor of (1+\varepsilon) for any \frac2n \le \varepsilon \le 1 must have at least {n}\choose{{\alpha}/{\varepsilon}} defining inequalities where 0<\alpha<1 is an absolute constant. This is tight as exhibited by the (1+\varepsilon) approximating linear ... more >>>