Farmer Pythagoras has a field in the shape of a right triangle. The right triangle's legs have lengths \(3\) and \(4\) units. In the corner where those sides meet at a right angle, he leaves a small unplanted square \(S\) so that from the air it looks like the right angle symbol. The rest of the field is planted. The shortest distance from \(S\) to the hypotenuse is \(2\) units. What fraction of the field is planted? The original answer is in \(\frac{m}{n}\) format, please give the value of \(m + n\).

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