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? $\textbf{(A) } \frac{25}{27} \qquad$ $ \textbf{(B) } \frac{26}{27} \qquad$ $ \textbf{(C) } \frac{73}{75} \qquad$ $ \textbf{(D) } \frac{145}{147} \qquad$ $ \textbf{(E) } \frac{74}{75}$