2024 Cayley Problem 19

In the diagram, \triangle ABC is right-angled at C. Points D, E, F are on AB, points G, H, J are on AC, point K is on EH, point L is on FJ, and point M is on BC so that DKHG, ELJH and FMCJ are squares. The area of DKHG is 16 and the area of ELJH is 36. The area of square FMCJ is

\textbf{(A)}\ 64\quad \textbf{(B)}\ 52\quad \textbf{(C)}\ 100\quad \textbf{(D)}\ 81\quad \textbf{(E)}\ 75

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.