document.write( "Question 1163079: please help me
\n" ); document.write( "What is the largest area that can be enclosed by fence? We have 180m of fence and there is a preexisting fence on one side.\r
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Algebra.Com's Answer #787046 by ikleyn(52814)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Since one side is just fenced, the total length of the three other sides of the rectangle, W, L an W is\r\n" );
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document.write( "L + 2W = 180 meters.\r\n" );
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document.write( "Hence, L = 180 - 2W meters.\r\n" );
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document.write( "    Area = Length * Width.\r\n" );
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document.write( "Substitute (180-2W) for L:\r\n" );
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document.write( "    A = W(180 - 2W)       (1)\r\n" );
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document.write( "    A = -2W^2 + 180W.\r\n" );
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document.write( "It is a quadratic function. It has the maximum at x = -b/(2a),  where \"a\"  is the coefficient at the quadratic term \r\n" );
document.write( "and  \"b\"  is the coefficient at the linear term, 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( "In your case, the maximum is at\r\n" );
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document.write( "    W = \"-180%2F%282%2A%28-2%29%29\" = \"%28-180%29%2F%28-4%29\" = 45.\r\n" );
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document.write( "So,  W = 45 meters is the width of the rectangle for the max area.\r\n" );
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document.write( "Then the length is  L = 180 - 2W = 180 - 2*45 = 90 meters.\r\n" );
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document.write( "So, the dimensions of the rectangle are 90 m and 45 m.\r\n" );
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document.write( "The max area is \r\n" );
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document.write( "    A = L*W = 90*45 = 4050 square meters.    ANSWER.\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
\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
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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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\n" ); document.write( "\n" ); document.write( "The most relevant to your problem is the lesson marked (*) in the list.\r
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\n" ); document.write( "\n" ); document.write( "My notice after reading the post by @Theo.\r
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\n" ); document.write( "\n" ); document.write( "            The original formulation in the post is absolutely and crystally clear.\r
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\n" ); document.write( "\n" ); document.write( "            The interpretations that @Theo tries to make,  to discuss and to use,  all are irrelevant and do not fit to the problem.\r
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\n" ); document.write( "\n" ); document.write( "            Simply ignore his post,  for your safety.\r
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