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2025 AMC 10B Question 13

AMC10 · 2025 AMC 10B

Question 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 $\dfrac{x}{x + y}?$
  1. $\dfrac{3}{7}$
  2. $\dfrac{\sqrt3}{4}$
  3. $\dfrac{4}{9}$
  4. $\dfrac{5}{11}$
  5. $\dfrac{4\sqrt3}{15}$