document.write( "Question 288985: A uniform-width boardwalk is built around the inside edge of a rectangular parkland that is 10m by 15m. If the boardwalk takes 20% of the lot, how wide is the boardwalk to the nearest centimetre? \n" ); document.write( "

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\n" ); document.write( "A uniform-width boardwalk is built around the inside edge of a rectangular parkland that is 10m by 15m.
\n" ); document.write( "If the boardwalk takes 20% of the lot, how wide is the boardwalk to the nearest centimetre?
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document.write( "Let x be the uniform wide of the boardwalk, in meters.\r\n" );
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document.write( "The area inside the boardwalk is  0.75*10*15 = 120 square meters.\r\n" );
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document.write( "Therefore, our equation for this area is\r\n" );
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document.write( "    (10-2x)*(15-2x) = 120.\r\n" );
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document.write( "Simplify and reduce it to the standard form quadratic equation\r\n" );
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document.write( "    150 - 50x + 4x^2 = 120,\r\n" );
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document.write( "    4x^2 - 50x + 30 = 0,\r\n" );
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document.write( "    2x^2 - 25x + 15 = 0.\r\n" );
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document.write( "     = .\r\n" );
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document.write( "One root    is  about  11.86 meters, and it is too big to be a solution \r\n" );
document.write( "to the problem, so we reject it.\r\n" );
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document.write( "The other root    is about  0.63 meters, and it makes sense as a solution \r\n" );
document.write( "to the problem, so we accept it.\r\n" );
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document.write( "ANSWER.  The width of the boardwalk is about 63 centimeters.\r\n" );
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