document.write( "Question 418955: what would be the length of the long side of a golden rectangle if the short side is 24 inches \n" ); document.write( "

Algebra.Com's Answer #293062 by josmiceli(19441) $\"\"$ $\"About$

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call the short side $\"y\"$ and the long side $\"x\"$
\n" ); document.write( "For a golden rectangle:
\n" ); document.write( " $\"y%2Fx+=+x%2F%28y+%2B+x%29\"$
\n" ); document.write( "---------
\n" ); document.write( "given:
\n" ); document.write( " $\"y+=+24\"$ in
\n" ); document.write( " $\"+24%2Fx+=+x%2F%2824+%2B+x%29+\"$
\n" ); document.write( " $\"+24%2A%2824+%2B+x%29+=+x%5E2+\"$
\n" ); document.write( " $\"+576+%2B+24x+=+x%5E2+\"$
\n" ); document.write( " $\"x%5E2+-+24x+-+576+=+0\"$
\n" ); document.write( "Use quadratic formula
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"a+=+1\"$
\n" ); document.write( " $\"b+=+-24\"$
\n" ); document.write( " $\"c+=+-576\"$
\n" ); document.write( " $\"x+=+%28-%28-24%29+%2B-+sqrt%28+%28-24%29%5E2+-+4%2A1%2A%28-576%29+%29%29%2F%282%2A1%29+\"$
\n" ); document.write( " $\"x+=+%28+24+%2B-+sqrt%28+576++%2B+2304+%29%29%2F+2+\"$
\n" ); document.write( " $\"x+=+%28+24+%2B-+sqrt%28+2880+%29%29%2F+2+\"$
\n" ); document.write( " $\"x+=+%28+24+%2B-+24%2Asqrt%28+5+%29%29%2F+2+\"$
\n" ); document.write( " $\"x+=+24%2A%281+%2B+sqrt%285%29%29+%2F+2+\"$
\n" ); document.write( " $\"x+=+12%2A%281+%2B+sqrt%285%29%29+\"$ \n" ); document.write( "

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