2024 Cayley Problem 15

A rectangle has width x and length y, as shown in Figure 1. The rectangle is cut along the horizontal and vertical dotted lines in Figure 1 to produce four smaller rectangles as shown in Figure 2.

The sum of the perimeters of these four rectangles in Figure 2 is 24. The value of x+y is

\textbf{(A)}\ 6\quad \textbf{(B)}\ 8\quad \textbf{(C)}\ 9.6\quad \textbf{(D)}\ 12\quad \textbf{(E)}\ 16

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 Cayley contests here.