{"status": "success", "data": {"description_md": "In rectangle $ABCD, AB=5$ and $BC=3$. Points $F$ and $G$ are on $\\overline{CD}$ so that $DF=1$ and $GC=2$. Lines $AF$ and $BG$ intersect at $E$. Find the area of $\\triangle AEB$.\n\n<center>\n<img class=\"problem-image\" height=\"228\" src=\"https://latex.artofproblemsolving.com/8/b/4/8b4fceed0d7e03e19b1507f86778bc77a8b7f334.png\" width=\"228\"/>\n</center> \n\n$\\textbf{(A) } 10 \\qquad\\textbf{(B) } \\frac{21}{2} \\qquad\\textbf{(C) } 12 \\qquad\\textbf{(D) } \\frac{25}{2} \\qquad\\textbf{(E) } 15$", "description_html": "<p>In rectangle  <span class=\"katex--inline\">ABCD, AB=5</span>  and  <span class=\"katex--inline\">BC=3</span> . Points  <span class=\"katex--inline\">F</span>  and  <span class=\"katex--inline\">G</span>  are on  <span class=\"katex--inline\">\\overline{CD}</span>  so that  <span class=\"katex--inline\">DF=1</span>  and  <span class=\"katex--inline\">GC=2</span> . Lines  <span class=\"katex--inline\">AF</span>  and  <span class=\"katex--inline\">BG</span>  intersect at  <span class=\"katex--inline\">E</span> . Find the area of  <span class=\"katex--inline\">\\triangle AEB</span> .</p>\n<center>\n<img class=\"problem-image\" height=\"228\" src=\"https://latex.artofproblemsolving.com/8/b/4/8b4fceed0d7e03e19b1507f86778bc77a8b7f334.png\" width=\"228\"/>\n</center> \n<p> <span class=\"katex--inline\">\\textbf{(A) } 10 \\qquad\\textbf{(B) } \\frac{21}{2} \\qquad\\textbf{(C) } 12 \\qquad\\textbf{(D) } \\frac{25}{2} \\qquad\\textbf{(E) } 15</span> </p>\n<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": 3, "problem_name": "2003 AMC 10B Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc10B_p21", "prev": "/problem/03_amc10B_p19"}}