2012 AMC 8 Problems/Problem 17
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 smallest 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 | |
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