{"status": "success", "data": {"description_md": "Rectangle $ABCD$, pictured below, shares $50\\%$ of its area with square $EFGH$. Square $EFGH$ shares $20\\%$ of its area with rectangle $ABCD$. What is $\\frac{AB}{AD}$?\n\n$$<center><img class=\"problem-image\" alt='[asy] unitsize(1mm); defaultpen(linewidth(.8pt)+fontsize(8pt));  draw((0,0)--(0,25)--(25,25)--(25,0)--cycle); fill((0,20)--(0,15)--(25,15)--(25,20)--cycle,gray); draw((0,15)--(0,20)--(25,20)--(25,15)--cycle); draw((25,15)--(25,20)--(50,20)--(50,15)--cycle);  label(\"$A$\",(0,20),W); label(\"$B$\",(50,20),E); label(\"$C$\",(50,15),E); label(\"$D$\",(0,15),W); label(\"$E$\",(0,25),NW); label(\"$F$\",(25,25),NE); label(\"$G$\",(25,0),SE); label(\"$H$\",(0,0),SW); [/asy]' class=\"latexcenter\" height=\"148\" src=\"https://latex.artofproblemsolving.com/5/4/3/54371c10b04c0bcf5a86491a02c9b7ecf851cb2d.png\" width=\"272\"/></center>$$\n\n$\\textbf{(A)}\\ 4 \\qquad \\textbf{(B)}\\ 5 \\qquad \\textbf{(C)}\\ 6 \\qquad \\textbf{(D)}\\ 8 \\qquad \\textbf{(E)}\\ 10$\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>Rectangle  <span class=\"katex--inline\">ABCD</span> , pictured below, shares  <span class=\"katex--inline\">50\\%</span>  of its area with square  <span class=\"katex--inline\">EFGH</span> . Square  <span class=\"katex--inline\">EFGH</span>  shares  <span class=\"katex--inline\">20\\%</span>  of its area with rectangle  <span class=\"katex--inline\">ABCD</span> . What is  <span class=\"katex--inline\">\\frac{AB}{AD}</span> ?</p>&#10;<p> <span class=\"katex--display\">&lt;center&gt;&lt;img class=&#34;problem-image&#34; alt='[asy] unitsize(1mm); defaultpen(linewidth(.8pt)+fontsize(8pt));  draw((0,0)--(0,25)--(25,25)--(25,0)--cycle); fill((0,20)--(0,15)--(25,15)--(25,20)--cycle,gray); draw((0,15)--(0,20)--(25,20)--(25,15)--cycle); draw((25,15)--(25,20)--(50,20)--(50,15)--cycle);  label(&#34;$A$&#34;,(0,20),W); label(&#34;$B$&#34;,(50,20),E); label(&#34;$C$&#34;,(50,15),E); label(&#34;$D$&#34;,(0,15),W); label(&#34;$E$&#34;,(0,25),NW); label(&#34;$F$&#34;,(25,25),NE); label(&#34;$G$&#34;,(25,0),SE); label(&#34;$H$&#34;,(0,0),SW); [/asy]' class=&#34;latexcenter&#34; height=&#34;148&#34; src=&#34;https://latex.artofproblemsolving.com/5/4/3/54371c10b04c0bcf5a86491a02c9b7ecf851cb2d.png&#34; width=&#34;272&#34;/&gt;&lt;/center&gt;</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 4 \\qquad \\textbf{(B)}\\ 5 \\qquad \\textbf{(C)}\\ 6 \\qquad \\textbf{(D)}\\ 8 \\qquad \\textbf{(E)}\\ 10</span> </p>&#10;<hr><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>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "2010 AMC 12A Problem 3", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc12A_p04", "prev": "/problem/10_amc12A_p02"}}