document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=549019>Question 549019</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer wants to divide his plot of land into 4 equal parts. He then will fence it in with 750 feet of fencing. Find a function that models the total area of the four pens. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #357418 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=357418\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "You can't do this problem exactly as it is stated.  That is because there is no guarantee as to the shape of the plot of land.\r<BR>\n" );
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document.write( "Proceeding on the assumption that your problem should have read: \"A farmer wants to divide his <b><i>rectangular</i></b> plot of land into 4 equal parts...\" \r<BR>\n" );
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document.write( "Draw a rectangle. Construct a line segment with endpoints at the midpoints of the long sides of the rectangle.  Construct a line segment with endpoints at the midpoints of the short sides of the rectangle.  In sum, you will have 6 line segments that each measure one-half of the length of your rectangle and an additional 6 line segments that each measure one-half of the width of the rectangle.  Therefore the total measure of the the line segments is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 3l\ +\ 3w\">, and we are given that this total measure must be 750 feet, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3l\ +\ 3w\ =\ 750\">\r<BR>\n" );
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document.write( "which is to say\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ l\ +\ w\ =\ 250\">\r<BR>\n" );
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document.write( "which is to say\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ l\ =\ 250\ -\ w\">\r<BR>\n" );
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document.write( "Since the area of the original rectangle is given by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large A\ =\ lw\">, then your Area (as a function of the width of the rectangle) would be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A(w)\ =\ 250w\ -\ w^2\">\r<BR>\n" );
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document.write( "Of course, all bets are off if the original plot was in the shape of a parallelogram, trapezoid, or some other odd-ball quadrilateral, or an ellipse, or...?\r<BR>\n" );
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document.write( "The area of a square field so divided and fenced would be exactly:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 125^2\ =\ 15625\"> square feet.\r<BR>\n" );
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document.write( "Which, by the way, is the maximum possible area for any rectangular shaped field.\r<BR>\n" );
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document.write( "The area of a circular field so divided and fenced would be exactly:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \pi\left(\frac{375}{\pi\ +\ 2}\right)^2\">\r<BR>\n" );
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document.write( "Which is approximately\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 16711.6\"> square feet\r<BR>\n" );
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document.write( "and any other regular polygon (except an equilateral triangle) would have an area somewhere between those limits.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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