document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=785549>Question 785549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The perimeter of a rectangle is 30 m. If one side is x, express the area of the rectangle in terms of x. Show that there is no value of x such that the area is 60m^2.\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #477694 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=477694\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > = length of one side in meters<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > = length of the adjacent side in meters<BR>\n" );
document.write( "(one is the length  of the rectangle, and the other one is the width)<BR>\n" );
document.write( "The perimeter (in meters) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2y=30 ALIGN=MIDDLE  ALT=\"2x%2B2y=30\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=15 ALIGN=MIDDLE  ALT=\"x%2By=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=15-x ALIGN=MIDDLE  ALT=\"y=15-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The area is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area=x%2Ay ALIGN=MIDDLE  ALT=\"area=x%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15-x ALIGN=MIDDLE  ALT=\"15-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area=x%2815-x%29 ALIGN=MIDDLE  ALT=\"area=x%2815-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area=15x-x%5E2 ALIGN=MIDDLE  ALT=\"area=15x-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (area expressed in terms of x)<BR>\n" );
document.write( "THat is a quadratic function.<BR>\n" );
document.write( "It graphs as a parabola, and the vertex is a maximum.<BR>\n" );
document.write( "(It is realy a portion of a parabola, because we must only define it for<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3Cx%3C15 ALIGN=MIDDLE  ALT=\"0%3Cx%3C15\"   DISABLED_style= \"max-width:90%; height:auto;\" > to have positive numbers for width odf the rectangle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area=15x-x%5E2 ALIGN=MIDDLE  ALT=\"area=15x-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area=-x%5E2%2B15x-56.25%2B56.25 ALIGN=MIDDLE  ALT=\"area=-x%5E2%2B15x-56.25%2B56.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area=-%28x%5E2-15x-56.25%29%2B56.25 ALIGN=MIDDLE  ALT=\"area=-%28x%5E2-15x-56.25%29%2B56.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area=-%28x-7.5%29%5E2%2B56.25 ALIGN=MIDDLE  ALT=\"area=-%28x-7.5%29%5E2%2B56.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum area is found when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7.5 ALIGN=MIDDLE  ALT=\"x=7.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56.25 ALIGN=MIDDLE  ALT=\"56.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "At that point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=15-7.5=7.5 ALIGN=MIDDLE  ALT=\"y=15-7.5=7.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the rectangle is a square.<BR>\n" );
document.write( "For any other value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, tyhe area is less than that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-7.5%29%5E2%3E0 ALIGN=MIDDLE  ALT=\"%28x-7.5%29%5E2%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x-7.5%29%5E2%3C0 ALIGN=MIDDLE  ALT=\"-%28x-7.5%29%5E2%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=area=-%28x-7.5%29%5E2%2B56.25%3C56.25 ALIGN=MIDDLE  ALT=\"area=-%28x-7.5%29%5E2%2B56.25%3C56.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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