{"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": "<p>A square with side length <span class=\"katex--inline\">x</span> is inscribed in a right triangle with sides of length <span class=\"katex--inline\">3</span>, <span class=\"katex--inline\">4</span>, and <span class=\"katex--inline\">5</span> so that one vertex of the square coincides with the right-angle vertex of the triangle. A square with side length <span class=\"katex--inline\">y</span> is inscribed in another right triangle with sides of length <span class=\"katex--inline\">3</span>, <span class=\"katex--inline\">4</span>, and <span class=\"katex--inline\">5</span> so that one side of the square lies on the hypotenuse of the triangle. What is <span class=\"katex--inline\">\\tfrac{x}{y}</span>?</p>&#10;<p><span class=\"katex--inline\">\\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}</span></p>&#10;", "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"}}