document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=426053>Question 426053</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the length and width of a rectangle that has the given perimeter and a maximum area.<BR>\n" );
document.write( "Perimeter: 48 meters  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #296486 by </B><A HREF=/tutors/aboutme.mpl?userid=Gogonati><B>Gogonati(855)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Gogonati><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=Gogonati><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=296486\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solution:Denote the length of rectangle  x m, since the perimeter is 48m then the width of rectangle is (24-x)m. We know that the area of rectangle is:\r<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=x%2A%2824-x%29 ALIGN=MIDDLE  ALT=\"A=x%2A%2824-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-x%5E2%2B24x ALIGN=MIDDLE  ALT=\"A=-x%5E2%2B24x\"   DISABLED_style= \"max-width:90%; height:auto;\" > This function introduce a downward parabola.\r<BR>\n" );
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document.write( "We find the vertex of this parabola: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-24%29%2F%28-2%29=12 ALIGN=MIDDLE  ALT=\"x=%28-24%29%2F%28-2%29=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the length is 12m the width will be: 24-12=12m\r<BR>\n" );
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document.write( "We conclude that this rectangle has the maximum area when its shape is square of side 12m.\r<BR>\n" );
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document.write( " We  find the value of area for x=12m : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2812%29=-%2812%29%5E2%2B24%2A12 ALIGN=MIDDLE  ALT=\"A%2812%29=-%2812%29%5E2%2B24%2A12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%2812%29=144+m%5E2 ALIGN=MIDDLE  ALT=\"+A%2812%29=144+m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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