smc

For rectangle $ABCD$ with perimeter 20, the diagonal $AC$ is given by: $$AC=\sqrt{l^2+w^2}$$ To minimize $AC$, $l$ and $w$ should be equal (i.e., the rectangle is a square). Thus, $l=w=5$. So, the minimum $AC$ is: $$AC=\sqrt{5^2+5^2}=\boxed{\sqrt{50}}$$