document.write( "Question 1208158: A rectangle given is a golden rectangle.\r
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\n" ); document.write( "\n" ); document.write( "Rectangle BCDE is similar to rectangle ACDF.\r
\n" ); document.write( "\n" ); document.write( "a. Show that \r
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Algebra.Com's Answer #846379 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "We can't tell which rectangle is given as a golden rectangle. Plus, you\r\n" );
document.write( "didn't tell us what \" a \", and what, if anything, you are letting be 1.\r\n" );
document.write( "Probably English is not your first language.  That is OK!! It is my ONLY\r\n" );
document.write( "language. J\r\n" );
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document.write( "I will assume that rectangle ACDF is given as a golden rectangle, and I will\r\n" );
document.write( "assume that the length of a side of square ABEF is \" a \". the shorter side of\r\n" );
document.write( "rectangle BCDE is given as \" 1 \".  \r\n" );
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document.write( "By definition of 'golden rectangle':\r\n" );
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Rectangle BCDE is similar to rectangle ACDF.

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a. Show that
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document.write( "CROSS-MULTIPLY\r\n" );
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document.write( "  <-- use this in part (b)\r\n" );
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document.write( "Divide both sides by (a-1)\r\n" );
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b. Find the exact value of a(which will give you the golden ratio) by completing the square.

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document.write( "1. Get half of coefficient of a:   (-1)/2 = -1/2\r\n" );
document.write( "2. Square (-1/2), get +1/4\r\n" );
document.write( "3. Add to both sides\r\n" );
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document.write( "Factor left side into the square of a binomial:\r\n" );
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document.write( "Take square roots of both sides, using ± on right.\r\n" );
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document.write( "Since ' a ' is not negative, we discard the - sign:\r\n" );
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document.write( "That is the exact value of ' a ', the golden ratio.\r\n" );
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document.write( "Edwin

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