2007 AMC 8 Problems/Problem 22
Problem
A lemming sits at a corner of a square with side length meters. The lemming runs meters along a diagonal toward the opposite corner. It stops, makes a right turn and runs more meters. A scientist measures the shortest distance between the lemming and each side of the square. What is the average of these four distances in meters?
Solution 1
The shortest segments would be perpendicular to the square. The lemming went meters horizontally and meters vertically. No matter how much it went, the lemming would have been and meters from the sides and and meters from the remaining two. To find the average, add the lengths of the four segments and divide by four: .
- Note that from any point in the square, the average distance from one side to the other is half of the square's side length.
Solution 2
For any point in the square, the sum of its distance to the left edge and right edge is equal to , and the sum of its distance to the up edge and down edge is also equal to . Thus, the answer is , and the moving progress is misguide at all.
Video Solution
https://www.youtube.com/watch?v=0X3-nEEXHGo
See Also
2007 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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