document.write( "Question 1204421: Cynthia Besch wants to buy a rug for a room that is 27ft wide and 35ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 609 square feet of carpeting. What dimensions should the rug have? \n" ); document.write( "

Algebra.Com's Answer #840650 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Cynthia Besch wants to buy a rug for a room that is 27ft wide and 35ft long.
\n" ); document.write( "She wants to leave a uniform strip of floor around the rug.
\n" ); document.write( "She can afford to buy 609 square feet of carpeting. What dimensions should the rug have?
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document.write( "Let x be an unknown uniform width of the strip around the rug.\r\n" );
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document.write( "Then the dimensions of the rug are (27-2x) ft and (35-2x) ft.\r\n" );
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document.write( "The area equation is\r\n" );
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document.write( "    (27-2x)*(35-2x) = 609 sq. ft, the affordable area.\r\n" );
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document.write( "Simplify and find x\r\n" );
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document.write( "    27*35 - 70x - 54x + 4x^2 = 609\r\n" );
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document.write( "    4x^2 - 124x + 336 = 0\r\n" );
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document.write( "     x^2 - 31x + 84 = 0\r\n" );
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document.write( "Solve using the quadratic formula\r\n" );
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document.write( "     =  = \r\n" );
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document.write( "     =  = 28;   =  = 3.\r\n" );
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document.write( "First root   = 28 ft is too large value, and we deny it;  second root  = 3 is good: we accept it.\r\n" );
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document.write( "ANSWER.  The dimensions of the rug should be  27-2*3 = 21 ft  and  35-2*3 = 29 ft.\r\n" );
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