document.write( "Question 1200723: one side of a rectangle is 3cm longer than the other. The area of the rectangle is twice its perimeter .Find the dimensions of the rectangle Thank you \n" ); document.write( "

Algebra.Com's Answer #834926 by ikleyn(52782) $\"\"$ $\"About$

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\n" ); document.write( "one side of a rectangle is 3cm longer than the other.
\n" ); document.write( "The area of the rectangle is twice its perimeter .
\n" ); document.write( "Find the dimensions of the rectangle Thank you
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document.write( "x = one side\r\n" );
document.write( "x+3 = the other side.\r\n" );
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document.write( "The area = x*(x+3)\r\n" );
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document.write( "The perimeter = 2(x + (x+3)) = 2(2x+3) = 4x + 6\r\n" );
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document.write( "Equation\r\n" );
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document.write( "    x*(x+3) = 2(4x + 6)\r\n" );
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document.write( "    x^2 + 3x - 8x - 12 = 0\r\n" );
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document.write( "    x^2 - 5x - 12 = 0\r\n" );
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document.write( "     =  = .\r\n" );
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document.write( "    The unique solution to the problem is the positive root x =  = 6.772001873.\r\n" );
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document.write( "The dimensions are 6.772001873 cm  and  9.772001873 cm.\r\n" );
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document.write( "CHECK.  The area is  6.772001873*9.772001873 = 66.17601499 cm^2;  \r\n" );
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document.write( "        the perimeter is  2*(6.772001873+9.772001873) = 33.08800749 cm.\r\n" );
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document.write( "        the ratio of these numbers is   = 2.000000000302  close enough to 2.\r\n" );
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