AHSME 1967 Problem 11

If the perimeter of rectangle $ABCD$ is $20$ inches, the least value of diagonal $\overline{AC}$, in inches, is: $\textbf{(A)}\ 0 \textbf{(B)}\ \sqrt{50} \textbf{(C)}\ 10 \textbf{(D)}\ \sqrt{200} \textbf{(E)}\ \text{none of these}$