Problem:
A regular hexagon and an equilateral triangle have equal areas. What is the ratio of the length of a side of the triangle to the length of a side of the hexagon?
Answer Choices:
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Solution:
The regular hexagon can be partitioned into six equilateral triangles, each with area one-sixth of the original triangle. Since the original equilateral triangle is similar to each of these, and the ratio of the areas is , it follows that the ratio of the sides is .