Let the sides of two rectangles be
![\{a,b\}](/media/m/d/4/1/d41bf8026ae4c3aa9a5069ca061bcb18.png)
and
![\{c,d\},](/media/m/c/5/3/c53a9bf378b62f9636be1db4cf537d74.png)
respectively, with
![a < c \leq d < b](/media/m/f/a/8/fa842b4a62d241f7f6e69c8f4583a545.png)
and
![ab < cd.](/media/m/a/e/e/aee65798cc3b45ddcb6ad73a50fb1a25.png)
Prove that the first rectangle can be placed within the second one if and only if
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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
$$\left(b^2 - a^2\right)^2 \leq \left(bc - ad \right)^2 + \left(bd - ac \right)^2.$$