2001 AMC 10 Problems/Problem 15
Contents
Problem
A street has parallel curbs feet apart. A crosswalk bounded by two parallel stripes crosses the street at an angle. The length of the curb between the stripes is feet and each stripe is feet long. Find the distance, in feet, between the stripes.
Solution 1
Drawing the problem out, we see we get a parallelogram with a height of and a base of , giving an area of .
If we look at it the other way, we see the distance between the stripes is the height and the base is .
The area is still the same, so the distance between the stripes is .
Solution 2
Alternatively, we could use similar triangles--the triangle (created by the length of the bordering stripe and the difference between the two curbs) is similar to the triangle, where we are trying to find (the shortest distance between the two stripes). Therefore, would have to be .
See Also
2001 AMC 10 (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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