{"status": "success", "data": {"description_md": "A paper triangle with sides of lengths $3,4,$ and $5$ inches, as shown, is folded so that point $A$ falls on point $B$. What is the length in inches of the crease?<br><center><img class=\"problem-image\" alt='[asy] draw((0,0)--(4,0)--(4,3)--(0,0)); label(\"$A$\", (0,0), SW); label(\"$B$\", (4,3), NE); label(\"$C$\", (4,0), SE); label(\"$4$\", (2,0), S); label(\"$3$\", (4,1.5), E); label(\"$5$\", (2,1.5), NW); fill(origin--(0,0)--(4,3)--(4,0)--cycle, gray); [/asy]' class=\"latexcenter\" height=\"198\" src=\"https://latex.artofproblemsolving.com/2/1/1/21145c9f39a3f3cd34317f8b1f8e3f3541c3c477.png\" width=\"252\"/></center>\n\n$\\textbf{(A) }   1+\\frac12 \\sqrt2   \\qquad        \\textbf{(B) }   \\sqrt3   \\qquad    \\textbf{(C) }   \\frac74   \\qquad   \\textbf{(D) }  \\frac{15}{8} \\qquad  \\textbf{(E) }   2$\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 paper triangle with sides of lengths  <span class=\"katex--inline\">3,4,</span>  and  <span class=\"katex--inline\">5</span>  inches, as shown, is folded so that point  <span class=\"katex--inline\">A</span>  falls on point  <span class=\"katex--inline\">B</span> . What is the length in inches of the crease?<br/><center><img class=\"latexcenter\" alt=\"[asy] draw((0,0)--(4,0)--(4,3)--(0,0)); label(&#34;$A$&#34;, (0,0), SW); label(&#34;$B$&#34;, (4,3), NE); label(&#34;$C$&#34;, (4,0), SE); label(&#34;$4$&#34;, (2,0), S); label(&#34;$3$&#34;, (4,1.5), E); label(&#34;$5$&#34;, (2,1.5), NW); fill(origin--(0,0)--(4,3)--(4,0)--cycle, gray); [/asy]\" height=\"198\" src=\"https://latex.artofproblemsolving.com/2/1/1/21145c9f39a3f3cd34317f8b1f8e3f3541c3c477.png\" width=\"252\"/></center></p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }   1+\\frac12 \\sqrt2   \\qquad        \\textbf{(B) }   \\sqrt3   \\qquad    \\textbf{(C) }   \\frac74   \\qquad   \\textbf{(D) }  \\frac{15}{8} \\qquad  \\textbf{(E) }   2</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 11", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc12A_p12", "prev": "/problem/18_amc12A_p10"}}