2009 AMC 10B 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 two parallel sides differ by

25-15=10,

split evenly between the two triangles, so each isosceles right triangle has legs of length

5

and area

\dfrac12\cdot5^2=\dfrac{25}{2}.

Together the beds cover

25

square meters. The rectangle has length

25

and width

5,

so area

125.

The fraction is

\dfrac{25}{125}=\dfrac15.

Thus, the correct answer is C.

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