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

15

and

25

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,

so each triangle has legs

\dfrac{10}{2} = 5

and area

\dfrac{1}{2} \cdot 5^2 = \dfrac{25}{2}.

The two beds total

25.

The rectangle measures

25

5,

so its area is

125,

and the fraction occupied is

\dfrac{25}{125} = \dfrac{1}{5}.

Thus, the correct answer is C.

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