{"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?\n\n<center>\n<img class=\"problem-image\" height=\"78\" src=\"https://latex.artofproblemsolving.com/0/e/0/0e0eb295ca042287f3d625b9ac6eed49532ef1ab.png\" width=\"105\"/>\n</center><br>\n\n$\\mathrm{(A)}\\ 2\\qquad\\mathrm{(B)}\\ 2.25\\qquad\\mathrm{(C)}\\ 2.5\\qquad\\mathrm{(D)}\\ 2.7\\qquad\\mathrm{(E)}\\ 3$", "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?</p>&#10;<center>&#10;<img class=\"problem-image\" height=\"78\" src=\"https://latex.artofproblemsolving.com/0/e/0/0e0eb295ca042287f3d625b9ac6eed49532ef1ab.png\" width=\"105\"/>&#10;</center><br/>&#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;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2008 AMC 10A Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc10A_p15", "prev": "/problem/08_amc10A_p13"}}