document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1125382>Question 1125382</A>: <I><SPAN STYLE=\"word-break: break-all;\"> https://vle.mathswatch.co.uk/images/questions/question2408.png<BR>\n" );
document.write( "please help me, thanks :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #741699 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=741699\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if they're similar, then their sides are proportional.\r<BR>\n" );
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document.write( "that gets you x / 4x = (x + 2) / 48\r<BR>\n" );
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document.write( "cross multiply to get 48x = 4x * (x + 2)\r<BR>\n" );
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document.write( "simplify to get 48x = 4x^2 + 8x\r<BR>\n" );
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document.write( "subtract 48x from both sides to get 0 = 4x^2 + 8x - 48x\r<BR>\n" );
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document.write( "combine like terms to get 0 = 4x^2 - 40x\r<BR>\n" );
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document.write( "factor to get 0 = 4x * (x - 10)\r<BR>\n" );
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document.write( "solve for x to get x = 0 or x = 10\r<BR>\n" );
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document.write( "x = 0 is not good, so it has to be x = 10 or not at all.\r<BR>\n" );
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document.write( "when x = 10, the smaller figure is 10 by 12 and the larger figure is 40 by 48.\r<BR>\n" );
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document.write( "the sides are proportional, as they should be with similar figures.\r<BR>\n" );
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document.write( "10 / 40 = 12 / 48\r<BR>\n" );
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document.write( "cross multiply to get 480 = 480, confirming the ratios are equal which confirms that the sides are proportional.\r<BR>\n" );
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document.write( "your solution is that the width of the badge is 40 cm.\r<BR>\n" );
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document.write( "that's the larger pentagon that has the smaller pentagon as part of it, if i understand the problem correctly.\r<BR>\n" );
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