document.write( "Question 1208618: The perimeter of a rectangular price tag is 28 centimeters. The area is 40 square centimeters. What are the dimensions of the price tag? \n" ); document.write( "

Algebra.Com's Answer #846989 by ikleyn(52780) $\"\"$ $\"About$

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\n" ); document.write( "The perimeter of a rectangular price tag is 28 centimeters. The area is 40 square centimeters.
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document.write( "Let x be the length, y be the width.\r\n" );
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document.write( "Then x+y is half of the perimeter\r\n" );
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document.write( "    x + y = 28/2 = 14 cm.\r\n" );
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document.write( "The average of x and y is    = 14/2 = 7 cm,\r\n" );
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document.write( "and we can write for the sides x and y\r\n" );
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document.write( "    x = 7 + w,  y = 7 - w,\r\n" );
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document.write( "where w is some unknown deviation from the average.\r\n" );
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document.write( "To find w, use the area equation  xy = 40,  or,  which is the same\r\n" );
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document.write( "    (7+w)*(7-w) = 40.\r\n" );
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document.write( "Simplify and find w\r\n" );
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document.write( "    49 - w^2 = 40,\r\n" );
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document.write( "    w^2 = 49 - 40 = 9,\r\n" );
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document.write( "    w =  = 3.\r\n" );
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document.write( "Thus x = 7+3 = 10;  y = 7-3 = 4.\r\n" );
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document.write( "ANSWER.  The dimensions of the card are 10 cm (the length) and 4 cm (the width).\r\n" );
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