document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=125348>Question 125348</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The ancient Greeks thought that the most pleasing shape for a rectangle was one for which the ratio of the length to the width was 8 to 5, the golden ratio.  If the length of a rectangular painting is 2 feet longer than its width, then for what dimension would 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 #91863 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=91863\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm going to presume that you are expected to calculate this using 8 to 5 as an approximation of the golden ratio, even though the actual golden ratio is an irrational number expressed exactly by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Bsqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"%281%2Bsqrt%285%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let x be the unknown width, and then x + 2 would be the unknown length.  Since the sides must be in the proportion 8:5, we can write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%2Fx=8%2F5 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%2Fx=8%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Cross-multiplying:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B10=8x ALIGN=MIDDLE  ALT=\"5x%2B10=8x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x-8x=-10 ALIGN=MIDDLE  ALT=\"5x-8x=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x=-10 ALIGN=MIDDLE  ALT=\"-3x=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10%2F3 ALIGN=MIDDLE  ALT=\"x=10%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > giving us the width.  The length is two feet more, so the length is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F3%2B2=10%2F3%2B6%2F3=16%2F3 ALIGN=MIDDLE  ALT=\"10%2F3%2B2=10%2F3%2B6%2F3=16%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you are curious, write back and I'll send you the calculations using the correct value for the golden ratio. </SPAN>\n" );
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