Difference between revisions of "2023 AMC 10A Problems/Problem 4"

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Revision as of 15:11, 9 November 2023

Problem

A quadrilateral has all integer sides lengths, a perimeter of $26$, and one side of length $4$. What is the greatest possible length of one side of this quadrilateral?

\[\textbf{(A)}~9\qquad\textbf{(B)}~10\qquad\textbf{(C)}~11\qquad\textbf{(D)}~12\qquad\textbf{(E)}~13\]

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 $\frac{26}{2}-1=13-1=\text{\boxed{(D)12}}$.

~zhenghua

See Also

2023 AMC 10A (ProblemsAnswer KeyResources)
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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