Question

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?

$\dfrac18$

$\dfrac16$

$\dfrac15$

$\dfrac14$

$\dfrac13$

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.

2009 AMC 10B Problem 4

Solution:

Problem 4 in Other Years