document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209156>Question 1209156</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the diagram, BD=15 cm and DC=6 cm. Find the ratio of the area of the parallelogram to the area of Triangle ABC.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847747 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13215)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=847747\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "EF and DC are congruent.<br><BR>\n" );
document.write( "With all the given parallel line segments, triangles AEF, EBD, and ABC are all similar.<br><BR>\n" );
document.write( "Corresponding sides EF, BD, and BC of those three triangles have lengths 6, 15, and 21, so the ratio of similarity among the three triangles is 6:15:21, or 2:5:7.<br><BR>\n" );
document.write( "The ratio of the areas of the three triangles is the square of the ratio of similarity, which is 4:25:49.<br><BR>\n" );
document.write( "For convenience, let the areas of the three triangles be...<BR>\n" );
document.write( "AEF = 4x<BR>\n" );
document.write( "EBD = 25x<BR>\n" );
document.write( "ABC = 49x<br><BR>\n" );
document.write( "The parallelogram is triangle ABC, minus triangles AEF and EBD, so the area of the parallelogram is 49x-4x-25x = 20x.  So the ratio of the area of the parallelogram to the area of triangle ABC is 20x:49x = 20:49.<br><BR>\n" );
document.write( "ANSWER: 20:49<br><BR>\n" );
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