{"status": "success", "data": {"description_md": "A rectangular floor measures $a$ by $b$ feet, where $a$ and $b$ are positive integers with $b > a$. An artist paints a rectangle on the floor with the sides of the rectangle parallel to the sides of the floor. The unpainted part of the floor forms a border of width $1$ foot around the painted rectangle and occupies half of the area of the entire floor. How many possibilities are there for the ordered pair $(a,b)$?\n\n$\\textbf{(A)}\\ 1\\qquad\\textbf{(B)}\\ 2\\qquad\\textbf{(C)}\\ 3\\qquad\\textbf{(D)}\\ 4\\qquad\\textbf{(E)}\\ 5$<br>([[2008 AMC 12B Problems/Problem 16|Solution]])\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>A rectangular floor measures  <span class=\"katex--inline\">a</span>  by  <span class=\"katex--inline\">b</span>  feet, where  <span class=\"katex--inline\">a</span>  and  <span class=\"katex--inline\">b</span>  are positive integers with  <span class=\"katex--inline\">b &gt; a</span> . An artist paints a rectangle on the floor with the sides of the rectangle parallel to the sides of the floor. The unpainted part of the floor forms a border of width  <span class=\"katex--inline\">1</span>  foot around the painted rectangle and occupies half of the area of the entire floor. How many possibilities are there for the ordered pair  <span class=\"katex--inline\">(a,b)</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 1\\qquad\\textbf{(B)}\\ 2\\qquad\\textbf{(C)}\\ 3\\qquad\\textbf{(D)}\\ 4\\qquad\\textbf{(E)}\\ 5</span> <br/>([[2008 AMC 12B Problems/Problem 16|Solution]])</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": 3, "problem_name": "2008 AMC 12B Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc12B_p17", "prev": "/problem/08_amc12B_p15"}}