{"status": "success", "data": {"description_md": "\nRectangle $ABCD$, 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![[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]](https://latex.artofproblemsolving.com/5/4/3/54371c10b04c0bcf5a86491a02c9b7ecf851cb2d.png)\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  50% of its area with square  <span class=\"katex--inline\">EFGH</span>. Square  <span class=\"katex--inline\">EFGH</span>  shares 20% of its area with rectangle <span class=\"katex--inline\">ABCD</span>. What is <span class=\"katex--inline\">\\frac{AB}{AD}</span>?<br/>&#10;<img src=\"https://latex.artofproblemsolving.com/5/4/3/54371c10b04c0bcf5a86491a02c9b7ecf851cb2d.png\" 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;&#34;,(0,20),W); label(&#34;&#34;,(50,20),E); label(&#34;&#34;,(50,15),E); label(&#34;&#34;,(0,15),W); label(&#34;&#34;,(0,25),NW); label(&#34;&#34;,(25,25),NE); label(&#34;&#34;,(25,0),SE); label(&#34;&#34;,(0,0),SW); [/asy]\"/></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/>&#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": "2010 AMC 12A Problem 3", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc12A_p04", "prev": "/problem/10_amc12A_p02"}}