Difference between revisions of "2007 AMC 8 Problems/Problem 22"
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Revision as of 01:29, 5 July 2013
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
Algebraic: 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:
.
See Also
2007 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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