2015 Gauss 8 Problem 16

There is a square whose perimeter is the same as the perimeter of the triangle shown. The area of that square is

\textbf{(A)}\ 12.25\,\text{cm}^2\quad \textbf{(B)}\ 196\,\text{cm}^2\quad \textbf{(C)}\ 49\,\text{cm}^2\quad \textbf{(D)}\ 36\,\text{cm}^2\quad \textbf{(E)}\ 144\,\text{cm}^2

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 Gauss contests here.