document.write( "Question 1205805: The area of a rectangular piece of cardboard is 1155. Its perimeter is 136. What is the length and the width.
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Algebra.Com's Answer #842844 by ikleyn(52782) $\"\"$ $\"About$

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document.write( "Since the perimeter is 136 units, half of the perimeter is 68 units.\r\n" );
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document.write( "Let x be the length.  Then the width is (68-x) units.\r\n" );
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document.write( "Equation for the area is length*width = 1155, or\r\n" );
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document.write( "    x*(68-x) = 1155.\r\n" );
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document.write( "Simplify to the standard form quadratic equation\r\n" );
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document.write( "    68x - x^2 = 1155\r\n" );
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document.write( "    x^2 - 68x - 1155 = 0.\r\n" );
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document.write( "Use the quadratic formula to find the roots\r\n" );
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document.write( "     =  =  = .\r\n" );
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document.write( "There are two roots, 35 and 33.\r\n" );
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document.write( "It gives 35 for the length (which is longer) and 68-35 = 33 for the width (which is shorter).\r\n" );
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document.write( "At this point, the problem is just solved in full.\r\n" );
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document.write( "ANSWER.  The length is 35 units.  The width is 33 units.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Memorize this method.
\n" ); document.write( "Million other similar problems can be solved in this way.\r
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