Problem:
A rectangular yard contains two flower beds in the shape of congruent isosceles right triangles. The remainder of the yard has a trapezoidal shape, as shown. The parallel sides of the trapezoid have lengths 15 and 25 meters. What fraction of the yard is occupied by the flower beds?
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Solution:
Each triangle has leg length meters and area square meters. Thus the flower beds have a total area of 25 square meters. The entire yard has length 25 and width 5 , so its area is 125 . The fraction of the yard occupied by the flower beds is .
The problems on this page are the property of the MAA's American Mathematics Competitions