A square with side length \(x\) is inscribed in a right triangle with sides of length \(3\), \(4\), and \(5\) so that one vertex of the square coincides with the right-angle vertex of the triangle. A square with side length \(y\) is inscribed in another right triangle with sides of length \(3\), \(4\), and \(5\) so that one side of the square lies on the hypotenuse of the triangle. Find the value of \(\dfrac{x}{y}\). 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{}.
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