document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1074737>Question 1074737</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular garden is fenced on three sides, and the house forms the fourth side of the rectangle. <BR>\n" );
document.write( "Given that the total length of the fence is 80m show that the area, A, of the garden is given by the formula A=y(80-2y), where you is the distance from the house to the end of the garden. <BR>\n" );
document.write( "Given that the area is a maximum for this length of fence, find the dimensions of the enclosed garden, and the area which is enclosed.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #689433 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=689433\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "The solution by \"josgarithmetic\" is &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28WRONG%29 ALIGN=MIDDLE  ALT=\"highlight%28WRONG%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Below find the correct solution.\r<BR>\n" );
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document.write( "The area of the garden, under the given condition, is\r\n" );
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document.write( "A = y*(80-2y) = -2y^2 + 80y.\r\n" );
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document.write( "Referring to the general form of a quadratic function\r\n" );
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document.write( "A = ay^2 + by +c,\r\n" );
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document.write( "the function have a maximum at y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F%282a%29 ALIGN=MIDDLE  ALT=\"-b%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-80%2F%282%2A%28-2%29%29 ALIGN=MIDDLE  ALT=\"-80%2F%282%2A%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%2F4 ALIGN=MIDDLE  ALT=\"90%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 20.\r\n" );
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document.write( "Thus the maximum is achieved at y = 20 m, and the maximal value of the quadratic function (of the area) is \r\n" );
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document.write( "A = -2*20^2 + 80*20 = -2*400 + 1600 = 800 square meters.\r\n" );
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document.write( "<U>Answer</U>.  The dimensions of the garden are 20 m x 40 m. Its area is 800 square meters.\r\n" );
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document.write( "The statement \r<BR>\n" );
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document.write( "     At given perimeter, the area of a rectangle is maximal if and only if the rectangle is a square\r\n" );
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document.write( "is true if the PERIMETER (the entire perimeter consisting of four sides) is constrained.\r<BR>\n" );
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document.write( "In the given problem we have ANOTHER/DIFFERENT situation.  (with which \"josgarithmetic\" is unfamiliar, due to his mathematical illiteracy).<BR>\n" );
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document.write( "Plot A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y%5E2+%2B+80y ALIGN=MIDDLE  ALT=\"-2y%5E2+%2B+80y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "On finding the maximum/minimum of a quadratic function see the lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>HOW TO complete the square to find the minimum/maximum of a quadratic function</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-How-to-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>Briefly on finding the minimum/maximum of a quadratic function</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-to-find-the-vertex-of-a-quadratic-function.lesson>HOW TO complete the square to find the vertex of a parabola</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-finding-the-vertex-of-a-parabola.lesson>Briefly on finding the vertex of a parabola</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/A-rectangle-with-the-given-perimeter-which-has-the-maximal-area-is-a-square.lesson>A rectangle with a given perimeter which has the maximal area is a square</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/A-farmer-planning-to-fence-a-rectangular-garden-to-enclose-the-maximal-area.lesson>A farmer planning to fence a rectangular garden to enclose the maximal area</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/A-farmer-planning-to-fence-a-rectangular-area-along-the-river--to-enclose-the-maximal-area.lesson>A farmer planning to fence a rectangular area along the river to enclose the maximal area</A> (*)\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/A-rancher-planning-to-fence-two-adjacent-rectangular-corrals-to-enclose-the-maximal-area-.lesson>A rancher planning to fence two adjacent rectangular corrals to enclose the maximal area</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/Using-quadratic-functions-to-solve-problems-on-maximizing-profit.lesson>Using quadratic functions to solve problems on maximizing revenue/profit</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this textbook under the topic \"<U>Finding minimum/maximum of quadratic functions</U>\". \r<BR>\n" );
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document.write( "In the list of lessons, one is marked by the (*) sign.<BR>\n" );
document.write( "It is your prototype/sample.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;H&nbsp;a&nbsp;p&nbsp;p&nbsp;y &nbsp;&nbsp;l&nbsp;e&nbsp;a&nbsp;r&nbsp;n&nbsp;i&nbsp;n&nbsp;g &nbsp;!&nbsp;!\r<BR>\n" );
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document.write( " </SPAN>\n" );
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