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Revision as of 15:11, 9 November 2023
Problem
A quadrilateral has all integer sides lengths, a perimeter of , and one side of length . What is the greatest possible length of one side of this quadrilateral?
Solution 1
Lets use the triangle inequality. We know that for a triangle, the 2 shorter sides must always be longer than the longest side. Similarly for a convex quadrilateral the shortest 3 sides must always be longer than the longest side. Thus the answer is .
~zhenghua
See Also
2023 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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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