document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=965124>Question 965124</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Not sure if \"topic\": selection is correct.\r<BR>\n" );
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document.write( "how do you figure out the smallest and largest possible perimeters of an area:\r<BR>\n" );
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document.write( "i.e.  (1) A picture frame has an area of 48 sq inches.  What is the largest possible perimeter of the pic frame?  (2) A backyard has an area of 64 sq feet.  What is the smallest possible perimeter of the backyard?\r<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 #589868 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</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=589868\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Question 1 is a rectangular shape that can be analyzed.  Question 2 shape is unspecified so is incomplete.\r<BR>\n" );
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document.write( "x and y dimensions of the rectangle.<BR>\n" );
document.write( "p for perimeter:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=2x%2B2y ALIGN=MIDDLE  ALT=\"p=2x%2B2y\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=48 ALIGN=MIDDLE  ALT=\"xy=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=2x%2B2%2848%2Fx%29 ALIGN=MIDDLE  ALT=\"p=2x%2B2%2848%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=2x%2B96%2Fx ALIGN=MIDDLE  ALT=\"p=2x%2B96%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The only method for minimizing or maximizing the perimeter seems to be derivatives.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dp%2Fdx=2%2B96%2A%28d%2Fdx%29%28x%5E%28-1%29%29 ALIGN=MIDDLE  ALT=\"dp%2Fdx=2%2B96%2A%28d%2Fdx%29%28x%5E%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=2%2B96%28-1%29%28x%5E-2%29 ALIGN=MIDDLE  ALT=\"2%2B96%28-1%29%28x%5E-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=2-96%2Fx%5E2 ALIGN=MIDDLE  ALT=\"2-96%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Finding extreme values, set derivative to zero.  Continue other steps.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dp%2Fdx=2-96%2Fx%5E2=0 ALIGN=MIDDLE  ALT=\"dp%2Fdx=2-96%2Fx%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=%282x%5E2-96%29%2Fx%5E2=0 ALIGN=MIDDLE  ALT=\"%282x%5E2-96%29%2Fx%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Denominator cannot be zero, and for derivative be zero, the NUMERATOR must be equated to zero.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-96=0 ALIGN=MIDDLE  ALT=\"2x%5E2-96=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%5E2-48=0 ALIGN=MIDDLE  ALT=\"x%5E2-48=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=48 ALIGN=MIDDLE  ALT=\"x%5E2=48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%2848%29 ALIGN=MIDDLE  ALT=\"x=sqrt%2848%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the positive value only.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%282%2A24%29=sqrt%282%2A2%2A6%2A2%29=sqrt%282%2A2%2A2%2A2%2A3%29 ALIGN=MIDDLE  ALT=\"x=sqrt%282%2A24%29=sqrt%282%2A2%2A6%2A2%29=sqrt%282%2A2%2A2%2A2%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=4%2Asqrt%283%29%29 ALIGN=MIDDLE  ALT=\"highlight%28x=4%2Asqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and from the original area equation, obviously <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"y=4%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, making the area shape as a SQUARE shape.  The values for MINIMUM perimeter.\r<BR>\n" );
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document.write( "Note that you will find this is for MAXIMUM area.  Check about the area equation and you should find no minimum.\r<BR>\n" );
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document.write( "Here is a graph for the PERIMETER equation, in one or either variable, here being <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=2x%2B48%2Fx ALIGN=MIDDLE  ALT=\"p=2x%2B48%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which shows a MINIMUM for the perimeter:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28350%2C350%2C-8%2C39%2C-8%2C39%2C2x%2B96%2Fx%29 ALIGN=MIDDLE  ALT=\"graph%28350%2C350%2C-8%2C39%2C-8%2C39%2C2x%2B96%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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