document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=164437>Question 164437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a rectangular storage area  is to be constructed along  the side of tall building, a security  fence is required along  the  remaning  three sides of the area. what is the maximum area that can be enclosed with 800 ft  of fencing. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121148 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=121148\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Call the side parallel to the building <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft<BR>\n" );
document.write( "Then the remaining 2 sides would each be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28800+-+x%29%2F2 ALIGN=MIDDLE  ALT=\"%28800+-+x%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft<BR>\n" );
document.write( "The area can then be expressed as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+x%2A%28800+-+x%29%2F2 ALIGN=MIDDLE  ALT=\"A+=+x%2A%28800+-+x%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%28800x+-+x%5E2%29+%2F+2 ALIGN=MIDDLE  ALT=\"A+=+%28800x+-+x%5E2%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+400x+-+x%5E2%2F2 ALIGN=MIDDLE  ALT=\"A+=+400x+-+x%5E2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a parabola which, because the coefficient of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is negative, has a maximum and not a minimum<BR>\n" );
document.write( "The maximum is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28b%2F2a%29 ALIGN=MIDDLE  ALT=\"-%28b%2F2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-%281%2F2%29 ALIGN=MIDDLE  ALT=\"a+=+-%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+400 ALIGN=MIDDLE  ALT=\"b+=+400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28b%2F2a%29+=+-%28400%2F-1%29 ALIGN=MIDDLE  ALT=\"-%28b%2F2a%29+=+-%28400%2F-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28400%29%2F-1+=+400 ALIGN=MIDDLE  ALT=\"-%28400%29%2F-1+=+400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum area is 400 ft2<BR>\n" );
document.write( "I'll check by finding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+400x+-+x%5E2%2F2 ALIGN=MIDDLE  ALT=\"A+=+400x+-+x%5E2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400+=+400x+-+x%5E2%2F2 ALIGN=MIDDLE  ALT=\"400+=+400x+-+x%5E2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2%2F2+%2B+400x+-+400+=+0 ALIGN=MIDDLE  ALT=\"-x%5E2%2F2+%2B+400x+-+400+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2+%2B+800x+-+800+=+0 ALIGN=MIDDLE  ALT=\"-x%5E2+%2B+800x+-+800+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-1 ALIGN=MIDDLE  ALT=\"a+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+800 ALIGN=MIDDLE  ALT=\"b+=+800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+-800 ALIGN=MIDDLE  ALT=\"c+=+-800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-800+%2B-+sqrt%28+800%5E2-4%2A%28-1%29%2A%28-800%29+%29%29%2F%282%2A%28-1%29%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-800+%2B-+sqrt%28+800%5E2-4%2A%28-1%29%2A%28-800%29+%29%29%2F%282%2A%28-1%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-800+%2B-+sqrt%28+640000+-+3200+%29%29%2F-2%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-800+%2B-+sqrt%28+640000+-+3200+%29%29%2F-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-800+%2B-+sqrt%28+636800+%29%29%2F-2%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-800+%2B-+sqrt%28+636800+%29%29%2F-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-800+%2B-+797.997%29%2F-2%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-800+%2B-+797.997%29%2F-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If I use the (+) value of the square root, I get too small a value<BR>\n" );
document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so I'll use the (-) square root<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1597.997%2F-2 ALIGN=MIDDLE  ALT=\"x+=+-1597.997%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+798.998 ALIGN=MIDDLE  ALT=\"x+=+798.998\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The remaining sides are <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.002%2F2+-+.501 ALIGN=MIDDLE  ALT=\"1.002%2F2+-+.501\"   DISABLED_style= \"max-width:90%; height:auto;\" >each<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+798.998%2A.501 ALIGN=MIDDLE  ALT=\"A+=+798.998%2A.501\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+400.297 ALIGN=MIDDLE  ALT=\"A+=+400.297\"   DISABLED_style= \"max-width:90%; height:auto;\" > The error is due to rounding off, I think\r<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );