{"status": "success", "data": {"description_md": "The diagram below shows a rectangle with side lengths $4$ and $8$ and a square with side length $5$. Three vertices of the square lie on three different sides of the rectangle, as shown. What is the area of the region inside both the square and the rectangle?<br><center><img class=\"problem-image\" alt='[asy] size(5cm); filldraw((4,0)--(8,3)--(8-3/4,4)--(1,4)--cycle,mediumgray); draw((0,0)--(8,0)--(8,4)--(0,4)--cycle,linewidth(1.1)); draw((1,0)--(1,4)--(4,0)--(8,3)--(5,7)--(1,4),linewidth(1.1)); label(\"$4$\", (8,2), E); label(\"$8$\", (4,0), S); label(\"$5$\", (3,11/2), NW); draw((1,.35)--(1.35,.35)--(1.35,0),linewidth(1.1)); [/asy]' class=\"latexcenter\" height=\"215\" src=\"https://latex.artofproblemsolving.com/6/4/5/645fb1f79da2019263c13108f385196fb1b0a8bd.png\" width=\"238\"/></center>\n\n$\\textbf{(A) }15\\dfrac{1}{8}  \\qquad<br>\\textbf{(B) }15\\dfrac{3}{8}  \\qquad<br>\\textbf{(C) }15\\dfrac{1}{2}  \\qquad<br>\\textbf{(D) }15\\dfrac{5}{8}  \\qquad<br>\\textbf{(E) }15\\dfrac{7}{8}$\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>The diagram below shows a rectangle with side lengths  <span class=\"katex--inline\">4</span>  and  <span class=\"katex--inline\">8</span>  and a square with side length  <span class=\"katex--inline\">5</span> . Three vertices of the square lie on three different sides of the rectangle, as shown. What is the area of the region inside both the square and the rectangle?<br/><center><img class=\"latexcenter\" alt=\"[asy] size(5cm); filldraw((4,0)--(8,3)--(8-3/4,4)--(1,4)--cycle,mediumgray); draw((0,0)--(8,0)--(8,4)--(0,4)--cycle,linewidth(1.1)); draw((1,0)--(1,4)--(4,0)--(8,3)--(5,7)--(1,4),linewidth(1.1)); label(&#34;$4$&#34;, (8,2), E); label(&#34;$8$&#34;, (4,0), S); label(&#34;$5$&#34;, (3,11/2), NW); draw((1,.35)--(1.35,.35)--(1.35,0),linewidth(1.1)); [/asy]\" height=\"215\" src=\"https://latex.artofproblemsolving.com/6/4/5/645fb1f79da2019263c13108f385196fb1b0a8bd.png\" width=\"238\"/></center></p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }15\\dfrac{1}{8}  \\qquad\\textbf{(B) }15\\dfrac{3}{8}  \\qquad\\textbf{(C) }15\\dfrac{1}{2}  \\qquad\\textbf{(D) }15\\dfrac{5}{8}  \\qquad\\textbf{(E) }15\\dfrac{7}{8}</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": "2022 AMC 12B Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc12B_p14", "prev": "/problem/22_amc12B_p12"}}