Difference between revisions of "2012 AMC 8 Problems/Problem 17"
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Revision as of 16:37, 3 July 2013
Problem
A square with integer side length is cut into 10 squares, all of which have integer side length and at least 8 of which have area 1. What is the smallest possible value of the length of the side of the original square?
Solution
The first answer choice , can be eliminated since there must be squares with integer side lengths. We then test the next largest sidelength which is . The square with area can be partitioned into squares with area and two squares with area , which satisfies all the conditions of the problem. Therefore, the smallest possible value of the length of the side of the original square is .
See Also
2012 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.