document.write( "Question 282707: The area of a square is 12 more than its perimeter. Find the length of a side. \n" ); document.write( "

Algebra.Com's Answer #854179 by ikleyn(53742) $\"\"$ $\"About$

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\n" ); document.write( "The area of a square is 12 more than its perimeter. Find the length of a side.
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\n" ); document.write( "\n" ); document.write( " The solution in the post by @mananth is incorrect, since his setup equation is incorrect.\r
\n" ); document.write( "\n" ); document.write( " I came to bring a correct solution.\r
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document.write( "Let x be the side length of the square.\r\n" );
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document.write( "The setup equation is\r\n" );
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document.write( "    x^2 = 4x + 12,\r\n" );
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document.write( "according to the problem.\r\n" );
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document.write( "Reduce it to the standard form of a quadratic equation and factorize\r\n" );
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document.write( "    x^2 - 4x - 12 = 0,\r\n" );
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document.write( "    (x-6)*(x+2) = 0.\r\n" );
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document.write( "The roots are x= 6  and  x= -2.\r\n" );
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document.write( "Since we look for a side length, we choose the positive root and reject the negative one.\r\n" );
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document.write( "ANSWER.  The side of the square is 6 units.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved correctly.\r
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\n" ); document.write( "\n" ); document.write( "You may check mentally that the answer value satisfies the problem's condition.\r
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