ISL 1996 G6

Let the sides of two rectangles be $\{a,b\}$ and $\{c,d\},$ respectively, with $a < c \leq d < b$ and $ab < cd.$ Prove that the first rectangle can be placed within the second one if and only if

$$\left(b^2 - a^2\right)^2 \leq \left(bc - ad \right)^2 + \left(bd - ac \right)^2.$$