Question 15
G6 (ARM) Let the sides of two rectangles be $\{a,b\}$ and $\{c,d\}$ with $a\lt c\le d\lt b$ and $ab\lt cd$. Prove that the first rectangle can be placed within the second one if and only if
$$(b^2-a^2)^2\le(bd-ac)^2+(bc-ad)^2.$$
$$(b^2-a^2)^2\le(bd-ac)^2+(bc-ad)^2.$$