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2001 AMC 10 Problem 15

Problem 15 of 25IntermediateGeometry

A street has parallel curbs 4040 feet apart. A crosswalk bounded by two parallel stripes crosses the street at an angle. The length of the curb between the stripes is 1515 feet and each stripe is 5050 feet long. Find the distance, in feet, between the stripes.

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Solution

The crosswalk is a parallelogram. Using the curb (1515 ft) as base and the street width (4040 ft) as height, its area is 1540=60015\cdot40=600 square feet. Using a stripe (5050 ft) as base, the area equals 5050 times the distance dd between the stripes, so d=60050=12.d=\frac{600}{50}=12. Thus, the correct answer is C.

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Concepts: parallelogram · area

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.