document.write( "Question 1157746: A rectangular field is to be enclosed by 400 m of fence. What is the maximum area? What dimensions will give the maximum area?\r
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Algebra.Com's Answer #780623 by ikleyn(52782)\"\" \"About 
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document.write( "Let x be the length of the rectangle and y be its width.\r\n" );
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document.write( "Then  x + y = \"400%2F2\" = 200,  and you are asked to find x and y in a way \r\n" );
document.write( "to maximize the product  x*y  which is the area.\r\n" );
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document.write( "Express y via x:  y = 200 - x,  and substitute it into the product:\r\n" );
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document.write( "    x*y = x*(200-x).\r\n" );
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document.write( "Next, find the maximum of the quadratic function  f(x) = x*(200-x) = \"-x%5E2+%2B+200x\".\r\n" );
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document.write( "
  Now let me remind you that, if you have a quadratic function f(x) = \"ax%5E2+%2B+bx+%2B+c\" of the general form,   \r\n" );
document.write( "    then it reaches the maximum/minimum at x = \"-b%2F2a\".
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document.write( "       See the lessons\r\n" );
document.write( "           - HOW TO complete the square to find the minimum/maximum of a quadratic function\r\n" );
document.write( "           - Briefly on finding the minimum/maximum of a quadratic function\r\n" );
document.write( "       in this site.\r\n" );
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document.write( "So, in our case the maximum is the vertex at x = \"-b%2F2a\" = \"%28-200%29%2F%28-2%29\" = 100.\r\n" );
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document.write( "Thus L = W = 100 meters, and the rectangle is actually a square with the area of 10000 m^2.\r\n" );
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\n" ); document.write( "\n" ); document.write( "My other relevant 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 area along the river 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
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-I in this site\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the topic \"Finding minimum/maximum of quadratic functions\". \r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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