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1988 AMC 12 Question 16

AMC12 · 1988 AMC 12

Question 16

$ABC$ and $A'B'C'$ are equilateral triangles with parallel sides and the same center, as in the figure. The distance between side $BC$ and side $B'C'$ is $\frac16$ the altitude of $\triangle ABC.$ The ratio of the area of $\triangle A'B'C'$ to the area of $\triangle ABC$ is

Question illustration
  1. $\frac1{36}$
  2. $\frac16$
  3. $\frac14$
  4. $\frac{\sqrt3}{4}$
  5. $\frac{9+8\sqrt3}{36}$