document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=894736>Question 894736</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rectangle R has varying length l and width w but with a constant perimeter of 4 feet.<BR>\n" );
document.write( "a)Express the area A as a function of length l<BR>\n" );
document.write( "Write a list of everything you know about this function.<BR>\n" );
document.write( "b)For what values of land w will the area of R be the greatest? <BR>\n" );
document.write( "Give an algebraic explanation. Then give a geometric explanation. Be sure to include a graph with relevant points labeled.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #542283 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=542283\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Length is L, width is w.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=wL ALIGN=MIDDLE  ALT=\"A=wL\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%2B2L=4 ALIGN=MIDDLE  ALT=\"2w%2B2L=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the constant perimeter of 4 feet.<BR>\n" );
document.write( "Simplify perimeter equation to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%2BL=2 ALIGN=MIDDLE  ALT=\"w%2BL=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Part (a) asks for A(L).<BR>\n" );
document.write( "from perimeter equation, w=2-L.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%282-L%29L ALIGN=MIDDLE  ALT=\"A=%282-L%29L\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2L-L%5E2 ALIGN=MIDDLE  ALT=\"A=2L-L%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Or if  you want, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A%28L%29=2L-L%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28A%28L%29=2L-L%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, area as a function of length.\r<BR>\n" );
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document.write( "The function A(L) is quadratic, and has a maximum value, based on coefficient on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2 ALIGN=MIDDLE  ALT=\"L%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > being <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The maximum value for area will be at L=w, meaning a square shape.  This will simply be L=1 and w=1; and the area will be 1 square foot.\r<BR>\n" );
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document.write( "Part (b): you asked for an algebraic explanation but I did not give it that way.  I simply gave a discussion.\r<BR>\n" );
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document.write( "Try this:<BR>\n" );
document.write( "Find roots for A(L).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2L-L%5E2=0 ALIGN=MIDDLE  ALT=\"2L-L%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%282-L%29=0 ALIGN=MIDDLE  ALT=\"L%282-L%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=0 ALIGN=MIDDLE  ALT=\"L=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=2 ALIGN=MIDDLE  ALT=\"L=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The maximum value occurs in the exact middle of these roots. </SPAN>\n" );
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