2025 AMC 10B Problem 13

The altitude to the hypotenuse of a 30-60-90^\circ right triangle is divided into two segments of lengths x \lt y by the median to the shortest side of the triangle. What is the ratio \dfrac{x}{x + y}?

\textbf{(A)} \dfrac{3}{7} \qquad \textbf{(B)} \dfrac{\sqrt3}{4} \qquad \textbf{(C)} \dfrac{4}{9} \qquad \textbf{(D)} \dfrac{5}{11} \qquad \textbf{(E)} \dfrac{4\sqrt3}{15}

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