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2018 AMC 10A Question 23

AMC10 · 2018 AMC 10A

Question 23

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?

Question illustration
  1. $\dfrac{25}{27}$
  2. $\dfrac{26}{27}$
  3. $\dfrac{73}{75}$
  4. $\dfrac{145}{147}$
  5. $\dfrac{74}{75}$