2023 AMC 10A Problem 4

A quadrilateral has all integer side 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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.