Assuming that the rectangles are congruent, let $x$ be the length of the longer side and $y$ be the length of the shorter sides.
We can then come up with the following system of equations:
$2x + y =20 $
$4y =16$
Solving for y gives us $y =4$ and adding that to our first equation gives us $\boxed{2x + 2y = 24}$.