AMC 12 2014b Problem 5

Doug constructs a square window using $8$ equal-size panes of glass, as shown. The ratio of the height to width for each pane is $5 : 2$, and the borders around and between the panes are $2$ inches wide. In inches, what is the side length of the square window?

fill((0,0)--(2,0)--(2,26)--(0,26)--cycle,gray);
fill((6,0)--(8,0)--(8,26)--(6,26)--cycle,gray);
fill((12,0)--(14,0)--(14,26)--(12,26)--cycle,gray);
fill((18,0)--(20,0)--(20,26)--(18,26)--cycle,gray);
fill((24,0)--(26,0)--(26,26)--(24,26)--cycle,gray);
fill((0,0)--(26,0)--(26,2)--(0,2)--cycle,gray);
fill((0,12)--(26,12)--(26,14)--(0,14)--cycle,gray);
fill((0,24)--(26,24)--(26,26)--(0,26)--cycle,gray);

\textbf{(A)}\ 26 \textbf{(B)}\ 28 \textbf{(C)}\ 30 \textbf{(D)}\ 32 \textbf{(E)}\ 34