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?

$\dfrac{1}{8}$

$\dfrac{1}{6}$

$\dfrac{1}{5}$

$\dfrac{1}{4}$

$\dfrac{1}{3}$

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 $25$ by $5,$ so its area is $125,$ and the fraction occupied is $\dfrac{25}{125} = \dfrac{1}{5}.$

Thus, the correct answer is C.

2009 AMC 12B Problem 4

Solution:

Problem 4 in Other Years