document.write( "Question 1189543: Boris has 320 meters of fencing. He will use it to form three sides of a rectangular garden. The fourth side will be along a house and will not need fencing.\r
\n" ); document.write( "\n" ); document.write( "(a) Find a function that gives the area A (x) of the garden (in square meters) in
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\n" ); document.write( "\n" ); document.write( "(b) What side length x gives the maximum area that the garden can have?
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Algebra.Com's Answer #820927 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "A farmer plans to fence a rectangular grazing area along a river with 300 yards of fence.
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document.write( "Since one side is the river, the rectangle's fence perimeter will be\r\n" );
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document.write( "    L + 2W = 300.\r\n" );
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document.write( "Hence, L = 300 - 2W.\r\n" );
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document.write( "    Area = Length * Width.\r\n" );
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document.write( "Substitute (300-2W) for L:\r\n" );
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document.write( "    A = W(300 - 2W)\r\n" );
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document.write( "    A = -2W^2 + 300W.\r\n" );
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document.write( "It is a quadratic function. It has the maximum at x = -b/(2a), according to the general theory.\r\n" );
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document.write( "    (See the lessons\r\n" );
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document.write( "         - HOW TO complete the square to find the minimum/maximum of a quadratic function\r\n" );
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document.write( "         - Briefly on finding the minimum/maximum of a quadratic function\r\n" );
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document.write( "     in this site).\r\n" );
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document.write( "For our quadratic function the maximum is at\r\n" );
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document.write( "    W =  =  = 75.\r\n" );
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document.write( "So, W = 75 yards is the width for max area.\r\n" );
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document.write( "Then the length is  L = 300 - 2W = 300 - 2*75 = 150 yards.\r\n" );
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document.write( "Find the maximum area. It is\r\n" );
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document.write( "    A = L*W = 150*75 = 11250 square yards.\r\n" );
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document.write( "The plot of the quadratic function for the area is shown below:  y = area and x = width.\r\n" );
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\n" ); document.write( "\n" ); document.write( "My other lessons in this site on finding the maximum/minimum of a quadratic function are \r
\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the vertex of a parabola\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the vertex of a parabola\r
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\n" ); document.write( "\n" ); document.write( "    - A rectangle with a given perimeter which has the maximal area is a square\r
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\n" ); document.write( "\n" ); document.write( "    - A farmer planning to fence a rectangular garden to enclose the maximal area\r
\n" ); document.write( "\n" ); document.write( "    - A rancher planning to fence two adjacent rectangular corrals to enclose the maximal area\r
\n" ); document.write( "\n" ); document.write( "    - Finding the maximum area of the window of a special form \r
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\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on finding the maximum/minimum of a quadratic function\r
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