document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=421354>Question 421354</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A dog owner has 250ft of fencing to enclose a rectangular run area for his dog. If he wants the maximun possible ares, what should the length and width of the rectangle be?\r<BR>\n" );
document.write( "\n" );
document.write( "i did 2x+2z=250 then got the equation 2z=250-2x using -b/2a i got -250/-4=62.5=x<BR>\n" );
document.write( "then 2z=250-2(62.5) and got z =62.5 which would mean each side is 62.5 and that checks out because 62.5*4=250 but how do i know thats the maximun area and also thats a square since all sides are equal?\r<BR>\n" );
document.write( "\n" );
document.write( " can anyone please please tell me what i did wrong or what i need to do?<BR>\n" );
document.write( "thank you!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #294265 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=294265\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A dog owner has 250ft of fencing to enclose a rectangular run area for his dog. If he wants the maximun possible ares, what should the length and width of the rectangle be? <BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "The max area for a rectangle is a square.<BR>\n" );
document.write( "The perimeter = 250 ft = 2L + 2W<BR>\n" );
document.write( "--> L + W = 125<BR>\n" );
document.write( "W = 125 - L<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "Area = L*W = L*(125 - L)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28L%29+=+125L+-+L%5E2 ALIGN=MIDDLE  ALT=\"f%28L%29+=+125L+-+L%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a parabola.  The max is at the vertex<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28L%29+=+-+L%5E2+%2B+125L ALIGN=MIDDLE  ALT=\"f%28L%29+=+-+L%5E2+%2B+125L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The line of symmetry is L = -b/2a<BR>\n" );
document.write( "L = 125/2 = 62.5<BR>\n" );
document.write( "The vertex is on the line of symmetry at f(-b/2a) = f(62.5)<BR>\n" );
document.write( "That proves that 62.5 ft gives the max area for the given perimeter.<BR>\n" );
document.write( "Max area = 62.5^2 = 3906.25 sq ft<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );