2021 Fermat Problem 13

In the diagram, each of \triangle WXZ and \triangle XYZ is an isosceles right-angled triangle. The length of WX is 6\sqrt{2}. The perimeter of quadrilateral WXYZ is closest to

\textbf{(A)}\ 18\quad \textbf{(B)}\ 20\quad \textbf{(C)}\ 23\quad \textbf{(D)}\ 25\quad \textbf{(E)}\ 29

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.