  Given a centered convex body $K\subseteq\mathbb{R}^n$, we study the optimal
value of the constant $\tilde{\Lambda}(K)$ such that there exists an
orthonormal basis $\{w_i\}_{i=1}^n$ for which the following reverse dual
Loomis-Whitney inequality holds: $$ |K|^{n-1}\leqslant
\tilde{\Lambda}(K)\prod_{i=1}^n|K\cap w_i^\perp|. $$ We prove that
$\tilde{\Lambda}(K)\leqslant(CL_K)^n$ for some absolute $C>1$ and that this
estimate in terms of $L_K$, the isotropic constant of $K$, is asymptotically
sharp in the sense that there exists another absolute constant $c>1$ and a
convex body $K$ such that
$(cL_K)^n\leqslant\tilde{\Lambda}(K)\leqslant(CL_K)^n$. We also prove more
general reverse dual Loomis-Whitney inequalities as well as reverse restricted
versions of Loomis-Whitney and dual Loomis-Whitney inequalities.
