Right triangles \(T_1\) and \(T_2\), have areas of \(1\) and \(2\), respectively. A side of \(T_1\) is congruent to a side of \(T_2\), and a different side of \(T_1\) is congruent to a different side of \(T_2\). Find the square of the product of the lengths of the other (third) sides of \(T_1\) and \(T_2\). The original answer is in \(\frac{k}{m}\) format, please give the value of k + m.

Let's think step by step and output the final answer within \boxed{}.
user