Problem:
An equilateral triangle is placed inside a larger equilateral triangle so that the region between them can be divided into three congruent trapezoids, as shown below. The side length of the inner triangle is the side length of the larger triangle. What is the ratio of the area of one trapezoid to the area of the inner triangle?
Answer Choices:
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Solution:
Since the inner triangle's side length is the side length of the outer triangle, its area is the area of the outer triangle. This means that the three trapezoids are the area of the outer triangle. Therefore, one trapezoid is the area of the outer triangle. This makes the ratio of the areas of one trapezoid and the inner triangle
Thus, is the correct answer.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions