document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=909230>Question 909230</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A home builder wants to build a rectangular deck on the back of the house. One side of the deck will share a wall with the house, and the other three sides will have a wooden railing. If the builder has enough wood for 15 meters of railing, what is the area of the largest deck he could build. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #551774 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=551774\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  A home builder wants to build a rectangular deck on the back of the house.<BR>\n" );
document.write( " One side of the deck will share a wall with the house, and the other three sides will have a wooden railing.<BR>\n" );
document.write( " If the builder has enough wood for 15 meters of railing, what is the area of the largest deck he could build.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Since one side is the length of the deck, we can write it<BR>\n" );
document.write( "L + 2W = 15<BR>\n" );
document.write( "L = (15-2w)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Area = L * W<BR>\n" );
document.write( "replace L with (15-2w)<BR>\n" );
document.write( "A = (15-2w)*W<BR>\n" );
document.write( "area is a function of w<BR>\n" );
document.write( "f(w) = -2w^2 + 15w<BR>\n" );
document.write( "The max area will be when w = the axis of symmetry x = (-b)/(2*a), so we have<BR>\n" );
document.write( "w = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-15%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"%28-15%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "w = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-15%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"%28-15%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "w = +3.75m the width for max area<BR>\n" );
document.write( "then<BR>\n" );
document.write( "15 - 2(3.75) = 7.5m is the length for max area<BR>\n" );
document.write( ":<BR>\n" );
document.write( "A = 7.5 * 3.75 = 28.125 sq/m is the max area </SPAN>\n" );
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