{"status": "success", "data": {"description_md": "In the diagram, square $PQRS$ is $3 \\times 3$. Points $T$ and $U$ are on side $QR$ with $QT = TU = UR = 1$. Points $V$ and $W$ are on side $RS$ with $RV = VW = WS = 1$. Line segments $TX$ and $UY$ are perpendicular to $QR$ and line segments $VY$ and $WX$ are perpendicular to $RS$. The ratio of the shaded area to the unshaded area is\n\n<center><img class=\"problem-image\" src=\"/static/cayley/2015/crops/15_cayley_p10_fig.png\" alt=\"figure\" width=\"230\"></center>\n\n$\\text{(A)}\\ 2:1\\qquad\\text{(B)}\\ 7:3\\qquad\\text{(C)}\\ 7:4\\qquad\\text{(D)}\\ 5:4\\qquad\\text{(E)}\\ 3:1$\n\n___\n\n**[Cayley](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "<p>In the diagram, square <span class=\"katex--inline\">PQRS</span> is <span class=\"katex--inline\">3 \\times 3</span>. Points <span class=\"katex--inline\">T</span> and <span class=\"katex--inline\">U</span> are on side <span class=\"katex--inline\">QR</span> with <span class=\"katex--inline\">QT = TU = UR = 1</span>. Points <span class=\"katex--inline\">V</span> and <span class=\"katex--inline\">W</span> are on side <span class=\"katex--inline\">RS</span> with <span class=\"katex--inline\">RV = VW = WS = 1</span>. Line segments <span class=\"katex--inline\">TX</span> and <span class=\"katex--inline\">UY</span> are perpendicular to <span class=\"katex--inline\">QR</span> and line segments <span class=\"katex--inline\">VY</span> and <span class=\"katex--inline\">WX</span> are perpendicular to <span class=\"katex--inline\">RS</span>. The ratio of the shaded area to the unshaded area is</p>\n<center><img class=\"problem-image\" src=\"/static/cayley/2015/crops/15_cayley_p10_fig.png\" alt=\"figure\" width=\"230\"></center>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 2:1\\qquad\\text{(B)}\\ 7:3\\qquad\\text{(C)}\\ 7:4\\qquad\\text{(D)}\\ 5:4\\qquad\\text{(E)}\\ 3:1</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Cayley</a>, by <a href=\"https://cemc.uwaterloo.ca/\">CEMC</a>, is licensed under the <a href=\"https://creativecommons.org/licenses/by-nc/3.0/\">CC BY-NC 3.0 DEED</a>. They are not affiliated with or endorse TopsOJ in any way.</strong></p>\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 1, "problem_name": "2015 Cayley Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/15_cayley_p11", "prev": "/problem/15_cayley_p09"}}