AMC 10 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?

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