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1968 AMC 12 Question 31

AMC12 · 1968 AMC 12

Question 31

In this diagram, not drawn to scale, figures $\mathrm{I}$ and $\mathrm{III}$ are equilateral triangular regions with respective areas of $32\sqrt3$ and $8\sqrt3$ square inches. Figure $\mathrm{II}$ is a square region with area $32$ square inches. Let the length of segment $AD$ be decreased by $12\dfrac12\%$ of itself, while the lengths of $AB$ and $CD$ remain unchanged. The percent decrease in the area of the square is:

Question illustration
  1. $12\dfrac12$
  2. $25$
  3. $50$
  4. $75$
  5. $87\dfrac12$