document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1125385>Question 1125385</A>: <I><SPAN STYLE=\"word-break: break-all;\"> https://vle.mathswatch.co.uk/images/questions/question17405.png please I need help with this homework and I cannot figure this out :) thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #741705 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=741705\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe the two rectangles are similar figures, therefore the corresponding sides are proportional.\r<BR>\n" );
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document.write( "this means that PQ / AB = QR / BC.\r<BR>\n" );
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document.write( "since PQ is 8 and QR is 2, then 8 / AB = 2 / BC.\r<BR>\n" );
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document.write( "cross multiply to get 8 * BC = 2 * AB\r<BR>\n" );
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document.write( "solve for AB to get AB= 4 * BC.\r<BR>\n" );
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document.write( "you are given that the perimeter of ABCD is 60.\r<BR>\n" );
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document.write( "this mean that 2 * BC + 2 * AB = 60\r<BR>\n" );
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document.write( "since AB = 4 * BC, this becomes 2 * BC + 2 * 4 * BC = 60\r<BR>\n" );
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document.write( "combine like terms to get 10 * BC = 60.\r<BR>\n" );
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document.write( "solve for BC to get BC = 6.\r<BR>\n" );
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document.write( "since AB = 4 * BC, then AB = 24.\r<BR>\n" );
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document.write( "the perimeter of ABCD is 60 which means that 2 * AB + 2 * BC = 60 which becomes 2 * 24 + 2 * 6 = 60 which becomes 48 + 12 = 60 which becomes 60 = 60.\r<BR>\n" );
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document.write( "this confirms the solution is correct.\r<BR>\n" );
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document.write( "in addition, the ratios are good because AB / PQ = 24 / 8 = 3 and BC / QR = 6/3 = 3.\r<BR>\n" );
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document.write( "the ratios are the same, confirming that the corresponding sides of the similar figures are proportinal.\r<BR>\n" );
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document.write( "your solution is that the length of AB is 24 and the length of BC is 6.\r<BR>\n" );
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document.write( "i think it could also be solved as follows:\r<BR>\n" );
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document.write( "the perimeter of PQRS is 2 * 8 + 2 * 2 = 16 + 4 = 20\r<BR>\n" );
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document.write( "the perimeter of ABCD is 60.\r<BR>\n" );
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document.write( "the rectangles are similar so the ratio of corresponding sides has to be the same.\r<BR>\n" );
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document.write( "the ratio of the perimeter is 60 / 20 = 3.\r<BR>\n" );
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document.write( "the corresponding sides of ABCD have to be 3 times the length of the corresponding sides of PQRS, therefore AB = 3 * 8 = 24 and BC = 3 * 2 = 6.\r<BR>\n" );
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document.write( "either way, i'm pretty sure that's the answer you're looking for.<BR>\n" );
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