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2009 AMC 12B Problem 4

Problem 4 of 25EasierGeometry

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 1515 and 2525 meters. What fraction of the yard is occupied by the flower beds?

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Solution

The parallel sides differ by 25−15=10,25 - 15 = 10, so each triangle has legs 102=5\dfrac{10}{2} = 5 and area 12⋅52=252.\dfrac{1}{2} \cdot 5^2 = \dfrac{25}{2}. The two beds total 25.25. The rectangle measures 2525 by 5,5, so its area is 125,125, and the fraction occupied is 25125=15.\dfrac{25}{125} = \dfrac{1}{5}. Thus, the correct answer is C.
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Tagged: area ratio · triangle area · trapezoid

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