AMC 12 2025 Part B Problem 10

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

Answer Choices:

A. \dfrac{3}{7}

B. \dfrac{\sqrt{3}}{4}

C. \dfrac{4}{9}

D. \dfrac{5}{11}

E. \dfrac{4\sqrt{3}}{15}