document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=807497>Question 807497</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( " Which has a greater area, a square with sides that are x - 1 units long or a rectangle with a length of x units and a width of x - 2 units?<BR>\n" );
document.write( "a.<BR>\n" );
document.write( "square<BR>\n" );
document.write( "b.<BR>\n" );
document.write( "rectangle<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 #486331 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=486331\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "For a given perimeter, a square is the greatest area rectangle that can be constructed.  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 4(x\ -\ 1)\ =\ 2x\ +\ 2(x\ -\ 2)\"> so your square and rectangle have the same perimeter.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P\ =\ 2l\ +\ 2w\">\r<BR>\n" );
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document.write( "so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ l\ =\ \frac{P}{2}\ -\ w\">\r<BR>\n" );
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document.write( "Since area is length times width\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A(w)\ =\ -w^2\ +\ \frac{P}{2}w\">\r<BR>\n" );
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document.write( "Since this is a quadratic function with a negative lead coefficient, the graph is a downward-opening parabola, hence the function value at the vertex represents a maximum value of the function.\r<BR>\n" );
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document.write( "The independent variable (<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large w\">) coordinate of the vertex is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ w_{max}\ =\ \frac{-\frac{P}{2}}{-2}\ =\ \frac{P}{4}\">\r<BR>\n" );
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document.write( "Therefore the maximum area is obtained when the width of the rectangle is the perimeter divided by 4.  If the perimeter divided by 4 is the width, 2 times the width is the perimeter divided by 2, and then 2 times the length must also be the perimeter divided by 2.  The four sides are equal in measure, and the maximum area figure is a square.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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