{"status": "success", "data": {"description_md": "Farmer Pythagoras has a field in the shape of a right triangle. The right triangle's legs have lengths $3$ and $4$ units. In the corner where those sides meet at a right angle, he leaves a small unplanted square $S$ so that from the air it looks like the right angle symbol. The rest of the field is planted. The shortest distance from $S$ to the hypotenuse is $2$ units. What fraction of the field is planted?<br><center><img class=\"problem-image\" alt='[asy] /* Edited by MRENTHUSIASM */ size(160); pair A, B, C, D, F; A = origin; B = (4,0); C = (0,3); D = (2/7,2/7); F = foot(D,B,C); fill(A--(2/7,0)--D--(0,2/7)--cycle, lightgray); draw(A--B--C--cycle); draw((2/7,0)--D--(0,2/7)); label(\"$4$\", midpoint(A--B), N); label(\"$3$\", midpoint(A--C), E); label(\"$2$\", midpoint(D--F), SE); label(\"$S$\", midpoint(A--D)); draw(D--F, dashed); [/asy]' class=\"latexcenter\" height=\"202\" src=\"https://latex.artofproblemsolving.com/6/b/5/6b5bfa5f42fc9840c0ffe1710ea05baf44b0dfbc.png\" width=\"268\"/></center>\n\n$\\textbf{(A) }   \\frac{25}{27}   \\qquad        \\textbf{(B) }   \\frac{26}{27}   \\qquad    \\textbf{(C) }   \\frac{73}{75}   \\qquad   \\textbf{(D) } \\frac{145}{147} \\qquad  \\textbf{(E) }   \\frac{74}{75}$\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>Farmer Pythagoras has a field in the shape of a right triangle. The right triangle&#8217;s legs have lengths  <span class=\"katex--inline\">3</span>  and  <span class=\"katex--inline\">4</span>  units. In the corner where those sides meet at a right angle, he leaves a small unplanted square  <span class=\"katex--inline\">S</span>  so that from the air it looks like the right angle symbol. The rest of the field is planted. The shortest distance from  <span class=\"katex--inline\">S</span>  to the hypotenuse is  <span class=\"katex--inline\">2</span>  units. What fraction of the field is planted?<br/><center><img class=\"latexcenter\" alt=\"[asy] /* Edited by MRENTHUSIASM */ size(160); pair A, B, C, D, F; A = origin; B = (4,0); C = (0,3); D = (2/7,2/7); F = foot(D,B,C); fill(A--(2/7,0)--D--(0,2/7)--cycle, lightgray); draw(A--B--C--cycle); draw((2/7,0)--D--(0,2/7)); label(&#34;$4$&#34;, midpoint(A--B), N); label(&#34;$3$&#34;, midpoint(A--C), E); label(&#34;$2$&#34;, midpoint(D--F), SE); label(&#34;$S$&#34;, midpoint(A--D)); draw(D--F, dashed); [/asy]\" height=\"202\" src=\"https://latex.artofproblemsolving.com/6/b/5/6b5bfa5f42fc9840c0ffe1710ea05baf44b0dfbc.png\" width=\"268\"/></center></p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }   \\frac{25}{27}   \\qquad        \\textbf{(B) }   \\frac{26}{27}   \\qquad    \\textbf{(C) }   \\frac{73}{75}   \\qquad   \\textbf{(D) } \\frac{145}{147} \\qquad  \\textbf{(E) }   \\frac{74}{75}</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": 3, "problem_name": "2018 AMC 12A Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc12A_p18", "prev": "/problem/18_amc12A_p16"}}