document.write( "Question 1161306: A square floor is fitted with rectangular tiles of perimeter 220cm. Each row (tile lengthwise) carries 20 less tiles than each column (tile breadth wise) if the length of the floor is 9.6m, calculate the dimensions of the tiles \n" ); document.write( "

Algebra.Com's Answer #784901 by ikleyn(52794) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " There is an elegant way to construct an equation and solve the problem.\r
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document.write( "Let w be the width of a tile, in centimeters (the same for all tiles).\r\n" );
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document.write( "Then the length of the a tile is 110-x centimeters (since 110 =  is half of the perimeter).\r\n" );
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document.write( "The number of tiles in each row (i.e. longwise) is  . \r\n" );
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document.write( "The number of tiles in each column              is  . \r\n" );
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document.write( "Second number is 20 more that the first one.  \r\n" );
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document.write( "It gives you this equation\r\n" );
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document.write( "     -  = 20.\r\n" );
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document.write( "It is your basic equation.\r\n" );
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document.write( "To solve it, first cancel the common factor 20 in both sides\r\n" );
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document.write( "     -  = 1.\r\n" );
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document.write( "Next multiply both sides by x*(110-x).  You will get\r\n" );
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document.write( "    48*(110-x) - 48*x = x*(110-x).\r\n" );
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document.write( "Simplify and reduce to the standard form quadratic equation\r\n" );
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document.write( "    48*110 - 48x - 48x = 110x - x^2\r\n" );
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document.write( "    x^2 - 206x + 5280 = 0.\r\n" );
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document.write( "At this point, you can solve this quadratic equation EITHER using the quadratic formula OR factoring\r\n" );
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document.write( "    (x-30)*(x+176) = 0.\r\n" );
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document.write( "This equation gives the only positive solution x= 30 centimeters.\r\n" );
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document.write( "ANSWER.  The dimensions of a tile are 30 cm (width) by (110-30) = 80 cm (length).\r\n" );
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