Estimating the diameter of the space of planar convex figures with respect to an affine-invariant metric

A convex figure $K\subset\mathbb R^2$ is a compact convex set with nonempty interior, and $\alpha K$ is a homothetic image of $K$ with coefficient $\alpha\in\mathbb R$. It is proved that for any two convex figures $K_1,K_2\subset\mathbb R^2$ there is an affine transformation $T$ of the plane such that $K_1\subset T(K_2)\subset2.7K_1$.