2015 Pascal Problem 17

In the diagram, six identical circles just touch the edges of rectangle PQRS and each circle just touches the adjacent circles. The centres T, V, W, Y of four of these circles form a smaller rectangle TVWY, as shown. The centres U and X lie on this rectangle. If the perimeter of TVWY is 60, what is the area of PQRS?

\textbf{(A)}\ 600\quad \textbf{(B)}\ 900\quad \textbf{(C)}\ 400\quad \textbf{(D)}\ 1200\quad \textbf{(E)}\ 1000

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 Pascal contests here.