document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=208674>Question 208674</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The golden ratio. The ancient Greeks thought that the<BR>\n" );
document.write( "most pleasing shape for a rectangle was one for which the<BR>\n" );
document.write( "ratio of the length to the width was approximately 8 to 5,<BR>\n" );
document.write( "the golden ratio. If the length of a rectangular painting is<BR>\n" );
document.write( "2 ft longer than its width, then for what dimensions would<BR>\n" );
document.write( "the length and width have the golden ratio? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157831 by </B><A HREF=/tutors/aboutme.mpl?userid=algebrapro18><B>algebrapro18(249)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=algebrapro18><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=157831\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Well the rectangular as width w and length w+2.  So now we set up a porportion to compare the two ratios and then solve for the width and then we can plug back in and find the length.\r<BR>\n" );
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document.write( "so our porportion will be\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28length-of-rectangle%29%2F%28width-of-rectangle%29+=+%28length-for-golden-ratio%29%2F%28width-for-golden-ratio%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now plugging in our expressions we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w%2B2%29%2F%28w%29+=+%288%29%2F%285%29 ALIGN=MIDDLE  ALT=\"%28w%2B2%29%2F%28w%29+=+%288%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we cross multiply and then solve the resulting equation:\r<BR>\n" );
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document.write( "5(w+2) = 8w<BR>\n" );
document.write( "5w+10 = 8w<BR>\n" );
document.write( "10 = 3w<BR>\n" );
document.write( "10/3 feet = w or w = 3.33333333333333333333333 feet\r<BR>\n" );
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document.write( "So now we find our length which we know is 2 feet + the width.  so l = 10/3 + 2 = 16/3 or 5.333333333333333\r<BR>\n" );
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