document.write( "Question 1157514: A rectangular field beside a river is to be fenced by 80 meters of fencing. No fence is needed along the riverbank. What are the dimensions of the field that maximize its area? \n" ); document.write( "
Algebra.Com's Answer #780393 by ikleyn(52787)\"\" \"About 
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document.write( "Since one side is the river, the rectangle's fence perimeter will be\r\n" );
document.write( "L + 2W = 80.\r\n" );
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document.write( "Hence, L = 80 - 2W.\r\n" );
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document.write( "Area = Length * Width.\r\n" );
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document.write( "Substitute (80-2W) for L:\r\n" );
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document.write( "    A = W(80 - 2W)\r\n" );
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document.write( "    A = -2W^2 + 80W.\r\n" );
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document.write( "This 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 = \"-80%2F%282%2A%28-2%29%29\" = \"%28-80%29%2F%28-4%29\" = 20.\r\n" );
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document.write( "So, W = 20 meters is the width for max area.\r\n" );
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document.write( "Then the length is  L = 80 - 2W = 80 - 2*20 = 40 meters\r\n" );
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document.write( "Find the max area. Substitute 20 for W\r\n" );
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document.write( "    A = -2(20^2) + 80*20 = 800 square meters.\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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document.write( "\"+graph%28+300%2C+200%2C+-50%2C+50%2C+-100%2C+1000%2C+-2x%5E2+%2B+80x%29+\" \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
\n" ); document.write( "\n" ); document.write( "    - A rectangle with a given perimeter which has the maximal area is a square\r
\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
\n" ); document.write( "\n" ); document.write( "    - Using quadratic functions to solve problems on maximizing revenue/profit\r
\n" ); document.write( "\n" ); document.write( "    - Minimal distance between sailing ships in a sea \r
\n" ); document.write( "\n" ); document.write( "    - Advanced lesson on finding minima of (x+1)(x+2)(x+3)(x+4) \r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on finding the maximum/minimum of a quadratic function\r
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\n" ); document.write( "\n" ); document.write( "Use this file/link  ALGEBRA-I - YOUR ONLINE TEXTBOOK  to navigate over all topics and lessons of the online textbook  ALGEBRA-I.\r
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