Difference between revisions of "2015 AMC 10A Problems/Problem 20"
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<math> \textbf{(A) }100\qquad\textbf{(B) }102\qquad\textbf{(C) }104\qquad\textbf{(D) }106\qquad\textbf{(E) }108 </math> | <math> \textbf{(A) }100\qquad\textbf{(B) }102\qquad\textbf{(C) }104\qquad\textbf{(D) }106\qquad\textbf{(E) }108 </math> | ||
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==Solution== | ==Solution== |
Revision as of 16:21, 31 January 2016
Problem
A square with positive integer side lengths in has area and perimeter . Which of the following numbers cannot equal ?
Solution
Let the rectangle's length and width be and . Its area is and the perimeter is .
Then . Factoring, this is .
Looking at the answer choices, only cannot be written this way, because then either or would be .
So the answer is .
See Also
2015 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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 AMC 10 Problems and Solutions |
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