  Let $\Omega$ be an open convex set in ${\mathbb R}^m$ with finite width, and
let $v_{\Omega}$ be the torsion function for $\Omega$, i.e. the solution of
$-\Delta v=1, v\in H_0^1(\Omega)$. An upper bound is obtained for the product
of $\Vert v_{\Omega}\Vert_{L^{\infty}(\Omega)}\lambda(\Omega)$, where
$\lambda(\Omega)$ is the bottom of the spectrum of the Dirichlet Laplacian
acting in $L^2(\Omega)$. The upper bound is sharp in the limit of a thinning
sequence of convex sets. For planar rhombi and isosceles triangles with area
$1$, it is shown that $\Vert v_{\Omega}\Vert_{L^{1}(\Omega)}\lambda(\Omega)\ge
\frac{\pi^2}{24}$, and that this bound is sharp.
