2007 AMC 8 Problem 22
Attempt Problem 22 of the 2007 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
22.
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?
Answer: C
Small hint:
For any point inside a square, distances to opposite sides add to the side length.
Big hint:
Apply that idea to both pairs of opposite sides.
Solution:
Based on the lengths given in the problem, the lemming is still in the square after it stops.
Since the lemming is still in the square, the sum of the distances to the horizontal sides is meters and the same for the vertical sides. Therefore, the distances sum to meters, making the average meters.
Thus, C is the correct answer.
Problem 22 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
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- 2006 AMC 8
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