document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1107699>Question 1107699</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A student is to mark out a rectangular field so that its perimeter is 400 metres. Let x be the length of the field. Find a formula for the area, A, of the field in terms of x and by graphing the formula on a number plane, find the dimensions of the field which would make the area a maximum.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #722722 by </B><A HREF=/tutors/aboutme.mpl?userid=addingup><B>addingup(3677)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=addingup><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=addingup><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=722722\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2L + 2W = 400<BR>\n" );
document.write( "simplifying:<BR>\n" );
document.write( "L + W = 200<BR>\n" );
document.write( "L = 200 - W <BR>\n" );
document.write( "Equation for the area:<BR>\n" );
document.write( "A = (200 - W) x W = 200W - W^2<BR>\n" );
document.write( "So we have a negative quadratic, which means we'll have an upside down parabola where the vertex is the maximum.<BR>\n" );
document.write( "Quadratic equation in the format y = ax2 + bx + c :<BR>\n" );
document.write( "A = –W^2 + 200W<BR>\n" );
document.write( "The vertex of the parabola is the point (h, k) where h = -b/2a:<BR>\n" );
document.write( "h = -200/(2 x (-1)) = -200/-2 = 100<BR>\n" );
document.write( "To find k, let's plug 100 for W:<BR>\n" );
document.write( "k = -100^2 + 200(100) = -10,000 + 20,000 = 10,000<BR>\n" );
document.write( "OK, so now we know that h (the maximizing width) is 100, and k (the maximum area) is 10,000. So the shape of our rectangle will be the square:<BR>\n" );
document.write( "2L + 2W = 400<BR>\n" );
document.write( "2(100) + 2(100) = 400<BR>\n" );
document.write( "----------------------------------------------<BR>\n" );
document.write( "NOTE: Of the rectangles (four sided figures with four right angles), the square will always give you the largest area.<BR>\n" );
document.write( "And of all geometric figures, the one that will give you the biggest area is the circle. IF your figure was a circle, the area you would get would be:<BR>\n" );
document.write( "A = C^2/4Pi where C is the perimeter<BR>\n" );
document.write( "A = 400^2/12.56 12,739<BR>\n" );
document.write( "Happy learning,<BR>\n" );
document.write( "John\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
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