1967 AHSME Problem 11

If the perimeter of rectangle ABCD is 20 inches, the least value of diagonal \overline{AC}, in inches, is:

\textbf{(A)}\ 0\qquad \textbf{(B)}\ \sqrt{50}\qquad \textbf{(C)}\ 10\qquad \textbf{(D)}\ \sqrt{200}\qquad \textbf{(E)}\ \text{none of these}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.