{"status": "success", "data": {"description_md": "\nFour congruent rectangles are placed as shown. The area of the outer square is  $4$ times that of the inner square. What is the ratio of the length of the longer side of each rectangle to the length of its shorter side?\n\n![[asy] unitsize(6mm); defaultpen(linewidth(.8pt));  path p=(1,1)--(-2,1)--(-2,2)--(1,2); draw(p); draw(rotate(90)*p); draw(rotate(180)*p); draw(rotate(270)*p); [/asy]](https://latex.artofproblemsolving.com/4/f/8/4f8d08abd119d663ad6630516ebc1b3bd784727e.png)\n\n$\\textbf{(A)}\\ 3 \\qquad \\textbf{(B)}\\ \\sqrt {10} \\qquad \\textbf{(C)}\\ 2 + \\sqrt2 \\qquad \\textbf{(D)}\\ 2\\sqrt3 \\qquad \\textbf{(E)}\\ 4$\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": "<p>Four congruent rectangles are placed as shown. The area of the outer square is  <span class=\"katex--inline\">4</span> times that of the inner square. What is the ratio of the length of the longer side of each rectangle to the length of its shorter side?</p>&#10;<p><img src=\"https://latex.artofproblemsolving.com/4/f/8/4f8d08abd119d663ad6630516ebc1b3bd784727e.png\" alt=\"[asy] unitsize(6mm); defaultpen(linewidth(.8pt));  path p=(1,1)--(-2,1)--(-2,2)--(1,2); draw(p); draw(rotate(90)*p); draw(rotate(180)*p); draw(rotate(270)*p); [/asy]\"/></p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ 3 \\qquad \\textbf{(B)}\\ \\sqrt {10} \\qquad \\textbf{(C)}\\ 2 + \\sqrt2 \\qquad \\textbf{(D)}\\ 2\\sqrt3 \\qquad \\textbf{(E)}\\ 4</span></p>&#10;<hr/>&#10;<p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "2009 AMC 12A Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc12A_p09", "prev": "/problem/09_amc12A_p07"}}