{"status": "success", "data": {"description_md": "A square with side length $x$ is inscribed in a right triangle with sides of length $3$, $4$, and $5$ so that one vertex of the square coincides with the right-angle vertex of the triangle. A square with side length $y$ is inscribed in another right triangle with sides of length $3$, $4$, and $5$ so that one side of the square lies on the hypotenuse of the triangle. What is $\\tfrac{x}{y}$?\n\n$\\textbf{(A) } \\dfrac{12}{13} \\qquad \\textbf{(B) } \\dfrac{35}{37} \\qquad \\textbf{(C) } 1 \\qquad \\textbf{(D) } \\dfrac{37}{35} \\qquad \\textbf{(E) } \\dfrac{13}{12}$", "description_html": "

A square with side length x is inscribed in a right triangle with sides of length 3 , 4 , and 5 so that one vertex of the square coincides with the right-angle vertex of the triangle. A square with side length y is inscribed in another right triangle with sides of length 3 , 4 , and 5 so that one side of the square lies on the hypotenuse of the triangle. What is \\tfrac{x}{y} ?

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\\textbf{(A) } \\dfrac{12}{13} \\qquad \\textbf{(B) } \\dfrac{35}{37} \\qquad \\textbf{(C) } 1 \\qquad \\textbf{(D) } \\dfrac{37}{35} \\qquad \\textbf{(E) } \\dfrac{13}{12}

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

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2017 AMC 10A Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc10A_p22", "prev": "/problem/17_amc10A_p20"}}