AHSME 1983 Problem 24

How many non-congruent right triangles are there such that the perimeter in $\text{cm}$ and the area in $\text{cm}^2$ are numerically equal? $\textbf{(A)} \ \text{none} \textbf{(B)} \ 1 \textbf{(C)} \ 2 \textbf{(D)} \ 4 \textbf{(E)} \ \text{infinitely many}$