document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=257085>Question 257085</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Billy has 52 m of fencing. He wishes to maximize the area of a rectangular garden. What are the dimensions of the rectangle he should use to maximize the area?<BR>\n" );
document.write( "What is the maximum area?<BR>\n" );
document.write( "If one side of the rectangular garden is a house and therefore will not require fancing, what dimensions should b used to maximize the area? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #189057 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=189057\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We have two formulas:<BR>\n" );
document.write( "(i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+2L+%2B+2W ALIGN=MIDDLE  ALT=\"P+=+2L+%2B+2W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+LW ALIGN=MIDDLE  ALT=\"A+=+LW\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the given information, (i) becomes<BR>\n" );
document.write( "(iii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52+=+2L+%2B+2W ALIGN=MIDDLE  ALT=\"52+=+2L+%2B+2W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "(iv) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26+=+L+%2B+W ALIGN=MIDDLE  ALT=\"26+=+L+%2B+W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving (iv) for L, we get<BR>\n" );
document.write( "(v) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+26+-+W ALIGN=MIDDLE  ALT=\"L+=+26+-+W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "substituting (v) into (ii) we get<BR>\n" );
document.write( "(vi) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%2826-W%29%28W%29 ALIGN=MIDDLE  ALT=\"A+=+%2826-W%29%28W%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "(vii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+-W%5E2+%2B+26W ALIGN=MIDDLE  ALT=\"A+=+-W%5E2+%2B+26W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "applying the quadratic, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28w-13%29%5E2+%2B+13%5E2 ALIGN=MIDDLE  ALT=\"-%28w-13%29%5E2+%2B+13%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so, the dimensions are 13 x 13 and the area is 169 sq. m.<BR>\n" );
document.write( "--<BR>\n" );
document.write( "If one side is a house, then<BR>\n" );
document.write( "(i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+L+%2B+2W ALIGN=MIDDLE  ALT=\"P+=+L+%2B+2W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+LW ALIGN=MIDDLE  ALT=\"A+=+LW\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From the given information, (i) becomes<BR>\n" );
document.write( "(iii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52+=+L+%2B+2W ALIGN=MIDDLE  ALT=\"52+=+L+%2B+2W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving (iii) for L, we get<BR>\n" );
document.write( "(iv) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+52+-+2W ALIGN=MIDDLE  ALT=\"L+=+52+-+2W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "substituting (iv) into (ii) we get<BR>\n" );
document.write( "(v) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%2852-2W%29%28W%29 ALIGN=MIDDLE  ALT=\"A+=+%2852-2W%29%28W%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "(vii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+-2W%5E2+%2B+52W ALIGN=MIDDLE  ALT=\"A+=+-2W%5E2+%2B+52W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "applying the quadratic, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%28w-13%29%5E2+%2B+52%5E2%2F8 ALIGN=MIDDLE  ALT=\"-2%28w-13%29%5E2+%2B+52%5E2%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so, the dimensions are 26 x 13 and the area is 338 sq. m. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );