{"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$\\textbf{(A)}\\ \\frac{12}{13} \\qquad \\textbf{(B)}\\ \\frac{35}{37} \\qquad\\textbf{(C)}\\ 1 \\qquad\\textbf{(D)}\\ \\frac{37}{35} \\qquad\\textbf{(E)}\\ \\frac{13}{12}$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "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} ?

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

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": 3, "problem_name": "2017 AMC 12A Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc12A_p20", "prev": "/problem/17_amc12A_p18"}}