1955 AHSME Problems/Problem 31
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:
The area of the large equilateral triangle is square units, so the smaller triangle is . The side length of the smaller length is . The median of the trapezoid can be determined by the average of the two bases of the trapezoids, so it works out to be units long.
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