2019 Fermat Problem 16

In the diagram, each line segment has length x or y. Also, each pair of adjacent sides is perpendicular.

If the area of the figure is 252 and x = 2y, the perimeter of the figure is

\textbf{(A)}\ 96\quad \textbf{(B)}\ 192\quad \textbf{(C)}\ 288\quad \textbf{(D)}\ 72\quad \textbf{(E)}\ 168

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.