The ratio of the short side of a certain rectangle to the long side is equal to the ratio of the long side to the diagonal. The original answer is in the form \(\frac{k\sqrt{m} - n}{p}\), where \(k\), \(m\), \(n\), and \(p\) are integers. What is the value of \(k + m + n + p\)?

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