AMC 12 2024b Problem 22

Let $\triangle ABC$ be a triangle with integer side lengths and the property that $\angle{B} = 2\angle{A}$. What is the least possible perimeter of such a triangle?

$\textbf{(A) }13 \textbf{(B) }14 \textbf{(C) }15 \textbf{(D) }16 \textbf{(E) }17$