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1988 AMC 12 Question 20

AMC12 · 1988 AMC 12

Question 20

In one of the adjoining figures a square of side $2$ is dissected into four pieces so that $E$ and $F$ are the midpoints of opposite sides and $AG$ is perpendicular to $BF.$ These four pieces can then be reassembled into a rectangle as shown in the second figure. The ratio of height to base, $\frac{XY}{YZ},$ in this rectangle is

Question illustration
  1. $4$
  2. $1+2\sqrt3$
  3. $2\sqrt5$
  4. $\frac{8+4\sqrt3}{3}$
  5. $5$