{"status": "success", "data": {"description_md": "Older television screens have an aspect ratio of $4: 3$. That is, the ratio of the width to the height is $4: 3$. The aspect ratio of many movies is not $4: 3$, so they are sometimes shown on a television screen by \"letterboxing\" - darkening strips of equal height at the top and bottom of the screen, as shown. Suppose a movie has an aspect ratio of $2: 1$ and is shown on an older television screen with a $27$-inch diagonal. What is the height, in inches, of each darkened strip?<br><center><img class=\"problem-image\" alt=\"[asy] unitsize(1mm); filldraw((0,0)--(21.6,0)--(21.6,2.7)--(0,2.7)--cycle,grey,black); filldraw((0,13.5)--(21.6,13.5)--(21.6,16.2)--(0,16.2)--cycle,grey,black); draw((0,0)--(21.6,0)--(21.6,16.2)--(0,16.2)--cycle); [/asy]\" class=\"latexcenter\" height=\"78\" src=\"https://latex.artofproblemsolving.com/0/e/0/0e0eb295ca042287f3d625b9ac6eed49532ef1ab.png\" width=\"105\"/></center>\n\n$\\mathrm{(A)}\\ 2\\qquad\\mathrm{(B)}\\ 2.25\\qquad\\mathrm{(C)}\\ 2.5\\qquad\\mathrm{(D)}\\ 2.7\\qquad\\mathrm{(E)}\\ 3$\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>Older television screens have an aspect ratio of  <span class=\"katex--inline\">4: 3</span> . That is, the ratio of the width to the height is  <span class=\"katex--inline\">4: 3</span> . The aspect ratio of many movies is not  <span class=\"katex--inline\">4: 3</span> , so they are sometimes shown on a television screen by &#8220;letterboxing&#8221; - darkening strips of equal height at the top and bottom of the screen, as shown. Suppose a movie has an aspect ratio of  <span class=\"katex--inline\">2: 1</span>  and is shown on an older television screen with a  <span class=\"katex--inline\">27</span> -inch diagonal. What is the height, in inches, of each darkened strip?<br/><center><img class=\"latexcenter\" alt=\"[asy] unitsize(1mm); filldraw((0,0)--(21.6,0)--(21.6,2.7)--(0,2.7)--cycle,grey,black); filldraw((0,13.5)--(21.6,13.5)--(21.6,16.2)--(0,16.2)--cycle,grey,black); draw((0,0)--(21.6,0)--(21.6,16.2)--(0,16.2)--cycle); [/asy]\" height=\"78\" src=\"https://latex.artofproblemsolving.com/0/e/0/0e0eb295ca042287f3d625b9ac6eed49532ef1ab.png\" width=\"105\"/></center></p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ 2\\qquad\\mathrm{(B)}\\ 2.25\\qquad\\mathrm{(C)}\\ 2.5\\qquad\\mathrm{(D)}\\ 2.7\\qquad\\mathrm{(E)}\\ 3</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": "2008 AMC 12A Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc12A_p10", "prev": "/problem/08_amc12A_p08"}}