A dielectric slab completely fills the space between the plates of a parallel-plate capacitor. The magnitude of the bound charge on each side of the slab is \(75 \%\) of the magnitude of the free charge on each plate. The capacitance is \(480 \epsilon_{0} \ell\), where \(\ell\) is a constant with dimensions of length, and the maximum charge that can be stored on the capacitor is \(240 \ell^{2} \epsilon_{0} E_{\max }\), where \(E_{\max }\) is the breakdown threshold. What are \((a)\) the dielectric constant for the slab, \((b)\) the plate separation distance in terms of \(\ell\), and (c) the plate area in terms of \(\ell\) ?