2012 AMC 8 Problem 17
Below is the video solution and professionally curated solution for Problem 17 of the 2012 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2012 AMC 8 solutions, or check the answer key.
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Difficulty rating: 1540
17.
A square with an 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?
Video solution:
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Written solution:
Since all the squares have integer side length, they each must have a side length greater than or equal to This means the total area must be over Therefore, the square can't have a side length less than or equal to or else it would have an area less than
We can make a configuration with side length however with the following configuration.
Thus, the answer is B .
Problem 17 in Other Years
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