Problem: An equilateral triangle whose side is is divided into a triangle and a trapezoid by a line drawn parallel to one of its sides. If the area of the trapezoid equals one-half of the area of the original triangle, the length of the median of the trapezoid is:
Answer Choices:
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Solution:
Let and denote the areas of the small and the original triangle, respectively. The median of the trapezoid is the arithmetic mean of the parallel sides, that is, , where denotes the shorter parallel side of the trapezoid. To find , observe that