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2023 AMC 12A Question 9

AMC12 · 2023 AMC 12A

Question 9

A square of area $2$ is inscribed in a square of area $3,$ creating four congruent triangles, as shown below. What is the ratio of the shorter leg to the longer leg in the shaded right triangle?

Question illustration
  1. $\dfrac{1}{5}$
  2. $\dfrac{1}{4}$
  3. $2-\sqrt{3}$
  4. $\sqrt{3}-\sqrt{2}$
  5. $\sqrt{2}-1$