AMC 12 2007b Problem 23

How many non-congruent right triangles with positive integer leg lengths have areas that are numerically equal to $3$ times their perimeters?

$\mathrm {(A)} 6 \mathrm {(B)} 7 \mathrm {(C)} 8 \mathrm {(D)} 10 \mathrm {(E)} 12$