document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=285794>Question 285794</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 #207207 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=207207\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Golden ratio is 8 to 5.<BR>\n" );
document.write( "This is the ratio of the length to the width.<BR>\n" );
document.write( "Length of the painting is 2 feet longer than its width.<BR>\n" );
document.write( "This means that L = W+2\r<BR>\n" );
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document.write( "If the ratio of the length to the width if 8:5, this means that:\r<BR>\n" );
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document.write( "L/W = 8/5\r<BR>\n" );
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document.write( "Cross multiply to get:\r<BR>\n" );
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document.write( "5L = 8W\r<BR>\n" );
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document.write( "If L = W+2, you can substitute in this equation to get:\r<BR>\n" );
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document.write( "5*(W+2) = 8W\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( "5W + 10 = 8W\r<BR>\n" );
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document.write( "Subtract 5W from both sides of this equation to get:\r<BR>\n" );
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document.write( "10 = 3W\r<BR>\n" );
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document.write( "Divide both sides of this equation by 3 to get:\r<BR>\n" );
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document.write( "W = 10/3 feet.\r<BR>\n" );
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document.write( "When W = 10/3 feet, L = W + 2 = 16/3\r<BR>\n" );
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document.write( "With L = 16/3 and W = 10/3, the ratio of L to W is equal to:\r<BR>\n" );
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document.write( "(16/3) / (10/3).\r<BR>\n" );
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document.write( "Multiply this faction by 3/3 and you get 16/10.\r<BR>\n" );
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document.write( "Multiply this fraction by (1/2)/(1/2) and you get:\r<BR>\n" );
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document.write( "8/5 which is the golden ratio.\r<BR>\n" );
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document.write( "The length and width will have the golden ration when the length = (16/3) and the width = (10/3).\r<BR>\n" );
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document.write( "Length of 16/3 is the same as 5.33333333.\r<BR>\n" );
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document.write( "Width of 10/3 is the same as 3.33333333.\r<BR>\n" );
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document.write( "Length is 2 feet longer than the width because 5.33333333 - 3.33333333 = 2.\r<BR>\n" );
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document.write( "ratio of Length to Width if 5.33333333/3.33333333 = 1.6 which is the same as 8/5.\r<BR>\n" );
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document.write( "That's your answer:\r<BR>\n" );
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document.write( "L = 5.33333333 = (16/3).<BR>\n" );
document.write( "W = 3.33333333 = (10/3).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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