2015 AMC 10A Problems/Problem 20
Contents
Problem
A rectangle with positive integer side lengths in has area and perimeter . Which of the following numbers cannot equal ?
Solution
Let the rectangle's length be and its width be . Its area is and the perimeter is .
Then . Factoring, we have .
The only one of the answer choices that cannot be expressed in this form is , as is twice a prime. There would then be no way to express as , keeping and as positive integers.
Our answer is then .
Note: The original problem only stated that and were positive integers, not the side lengths themselves. This rendered the problem unsolvable, and so the AMC awarded everyone 6 points on this problem. This wiki has the corrected version of the problem so that the 2015 AMC 10A test can be used for practice.
Video Solution
~savannahsolver
See Also
2015 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.