{"status": "success", "data": {"description_md": "In rhombus $ABCD$, point $P$ lies on segment $\\overline{AD}$ so that $\\overline{BP}$ $\\perp$ $\\overline{AD}$, $AP = 3$, and $PD = 2$. What is the area of $ABCD$? (Note: The figure is not drawn to scale.)<br><center><img class=\"problem-image\" alt='[asy] import olympiad; size(180); real r = 3, s = 5, t = sqrt(r*r+s*s); defaultpen(linewidth(0.6) + fontsize(10)); pair A = (0,0), B = (r,s), C = (r+t,s), D = (t,0), P = (r,0); draw(A--B--C--D--A^^B--P^^rightanglemark(B,P,D)); label(\"$A$\",A,SW); label(\"$B$\", B, NW); label(\"$C$\",C,NE); label(\"$D$\",D,SE); label(\"$P$\",P,S); [/asy]' class=\"latexcenter\" height=\"185\" src=\"https://latex.artofproblemsolving.com/1/5/0/150aeac95fbc38e4ea6602817ade871e681d99e3.png\" width=\"302\"/></center>\n\n$\\textbf{(A) }3\\sqrt 5 \\qquad<br>\\textbf{(B) }10 \\qquad<br>\\textbf{(C) }6\\sqrt 5 \\qquad<br>\\textbf{(D) }20\\qquad<br>\\textbf{(E) }25$\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>In rhombus  <span class=\"katex--inline\">ABCD</span> , point  <span class=\"katex--inline\">P</span>  lies on segment  <span class=\"katex--inline\">\\overline{AD}</span>  so that  <span class=\"katex--inline\">\\overline{BP}</span>   <span class=\"katex--inline\">\\perp</span>   <span class=\"katex--inline\">\\overline{AD}</span> ,  <span class=\"katex--inline\">AP = 3</span> , and  <span class=\"katex--inline\">PD = 2</span> . What is the area of  <span class=\"katex--inline\">ABCD</span> ? (Note: The figure is not drawn to scale.)<br/><center><img class=\"latexcenter\" alt=\"[asy] import olympiad; size(180); real r = 3, s = 5, t = sqrt(r*r+s*s); defaultpen(linewidth(0.6) + fontsize(10)); pair A = (0,0), B = (r,s), C = (r+t,s), D = (t,0), P = (r,0); draw(A--B--C--D--A^^B--P^^rightanglemark(B,P,D)); label(&#34;$A$&#34;,A,SW); label(&#34;$B$&#34;, B, NW); label(&#34;$C$&#34;,C,NE); label(&#34;$D$&#34;,D,SE); label(&#34;$P$&#34;,P,S); [/asy]\" height=\"185\" src=\"https://latex.artofproblemsolving.com/1/5/0/150aeac95fbc38e4ea6602817ade871e681d99e3.png\" width=\"302\"/></center></p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }3\\sqrt 5 \\qquad\\textbf{(B) }10 \\qquad\\textbf{(C) }6\\sqrt 5 \\qquad\\textbf{(D) }20\\qquad\\textbf{(E) }25</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": 2, "problem_name": "2022 AMC 12B Problem 2", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc12B_p03", "prev": "/problem/22_amc12B_p01"}}