1960 AHSME Problem 21

The diagonal of square I is a+b. The perimeter of square II with twice the area of I is:

\textbf{(A)}\ (a+b)^2\qquad \textbf{(B)}\ \sqrt{2}(a+b)^2\qquad \textbf{(C)}\ 2(a+b)\qquad \textbf{(D)}\ \sqrt{8}(a+b) \qquad \textbf{(E)}\ 4(a+b)

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