2001 AMC 10 Problem 15

Question

A street has parallel curbs

40

feet apart. A crosswalk bounded by two parallel stripes crosses the street at an angle. The length of the curb between the stripes is

15

feet and each stripe is

50

feet long. Find the distance, in feet, between the stripes.

9

10

12

15

25

The crosswalk is a parallelogram; compute its area using the curb as base

The same area equals stripe length times the distance between the stripes

The crosswalk is a parallelogram. Using the curb (

15

ft) as base and the street width (

40

ft) as height, its area is

15\cdot40=600

square feet.

Using a stripe (

50

ft) as base, the area equals

50

times the distance

d

between the stripes, so

d=\frac{600}{50}=12.

Thus, the correct answer is C.

Problem 15 in other years