2019 Pascal Problem 18

In the diagram, each of \triangle QPT, \triangle QTS and \triangle QSR is an isosceles, right-angled triangle, with \angle QPT = \angle QTS = \angle QSR = 90^\circ. The combined area of the three triangles is 56. If QP = PT = k, what is the value of k?

\textbf{(A)}\ \sqrt{2}\quad \textbf{(B)}\ 1\quad \textbf{(C)}\ 4\quad \textbf{(D)}\ 2\quad \textbf{(E)}\ 2\sqrt{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 Pascal contests here.