document.write( "Question 1100148: My friend has $270 to spend on a fence for her rectangular garden. She wants to use cedar fencing which costs $15/yard on one side, and cheaper metal fencing which costs $3/yard for the other three sides. What are the dimensions of the garden with the largest area she can enclose?
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Algebra.Com's Answer #714633 by ikleyn(52778) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Let x be the length in yards of the front fence (at 15 dollars per yard).\r\n" );
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document.write( "Then the other dimension will be  yards,  or   yards = (45 - 3x) yards.\r\n" );
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document.write( "The area is the product of these dimensions\r\n" );
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document.write( "Area A =  square yards.\r\n" );
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document.write( "And the problem asks to find the maximal area as the maximum of this quadratic form.\r\n" );
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document.write( "This quadratic form has the zeroes 0 and  = 15, so its maximum is achieved exactly at the midpoint between the zeroes, i.e at  x= 7.5.\r\n" );
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document.write( "Answer.  Under the given condition, the maximum area is the rectangle with one dimension 7.5 yards (front yard at $15/yard) \r\n" );
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document.write( "         and other dimension 45-3*7.5 = 22.5 yards.\r\n" );
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\n" ); document.write( "On finding minimum/maximum of quadratic functions and solving similar problems see the lessons\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 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
\n" ); document.write( "\n" ); document.write( "in this site.\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
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\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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