document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1026358>Question 1026358</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with the following word problem:<BR>\n" );
document.write( "The perimeter of a rectangle is 64 cm.\r<BR>\n" );
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document.write( "(a)  <BR>\n" );
document.write( "If the width of the rectangle is x cm, give a formula for y, the height of the rectangle in cm, in terms of x.\r<BR>\n" );
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document.write( "For this one I got y=32-x, but the answer is needed for part b so I thought I should include it.\r<BR>\n" );
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document.write( "(b)  <BR>\n" );
document.write( "Using your answer in part (a), give a formula for A, the area in cm^2, in terms of the width x.\r<BR>\n" );
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document.write( "For this one, I tried to substitute the formula for y into the equation for the perimeter: 2x+2y=64. This didn't work because when I substituted that formula into the equation, the equation didn't allow me to solve for y because it zeroed out.\r<BR>\n" );
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document.write( "(c)  <BR>\n" );
document.write( "Find the lengths of the sides of the rectangle giving the maximum area. What is the maximum area?\r<BR>\n" );
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document.write( "For this one, I couldn't do it since the substitution in the previous problem didn't help. I also don't understand what maximum area means. <BR>\n" );
document.write( "Thank you for the help and your time :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #641606 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=641606\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Width = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm<BR>\n" );
document.write( "perimeter  = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+64+ ALIGN=MIDDLE  ALT=\"+64+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+ ALIGN=MIDDLE  ALT=\"+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the length in cm<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "(a)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+%2B+2y+=+64+ ALIGN=MIDDLE  ALT=\"+2x+%2B+2y+=+64+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2y+=+64+-+2x+ ALIGN=MIDDLE  ALT=\"+2y+=+64+-+2x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+32+-+x+ ALIGN=MIDDLE  ALT=\"+y+=+32+-+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+ ALIGN=MIDDLE  ALT=\"+A+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = area in cm2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+x%2Ay+ ALIGN=MIDDLE  ALT=\"+A+=+x%2Ay+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "By substitution:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+x%2A%28++32+-+x+%29+ ALIGN=MIDDLE  ALT=\"+A+=+x%2A%28++32+-+x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+-x%5E2+%2B+32x+ ALIGN=MIDDLE  ALT=\"+A+=+-x%5E2+%2B+32x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "To understand maximum area, assume<BR>\n" );
document.write( "the perimeter doesn't change, but the<BR>\n" );
document.write( "width and length are allowed to change.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+64+ ALIGN=MIDDLE  ALT=\"+P+=+64+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+64+=++2%2A24+%2B+2%2A8+ ALIGN=MIDDLE  ALT=\"+64+=++2%2A24+%2B+2%2A8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This area is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+8%2A24+ ALIGN=MIDDLE  ALT=\"+A+=+8%2A24+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+192+ ALIGN=MIDDLE  ALT=\"+A+=+192+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm2<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Try different width and length:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+64+=+2%2A16+%2B+2%2A16+ ALIGN=MIDDLE  ALT=\"+64+=+2%2A16+%2B+2%2A16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+16%2A16+ ALIGN=MIDDLE  ALT=\"+A+=+16%2A16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+256+ ALIGN=MIDDLE  ALT=\"+A+=+256+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm2<BR>\n" );
document.write( "This area is larger with the same perimeter<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+-x%5E2+%2B+32x+ ALIGN=MIDDLE  ALT=\"+A+=+-x%5E2+%2B+32x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a parabola with a maximum. When the form is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+ax%5E2+%2B+bx+%2B+c+ ALIGN=MIDDLE  ALT=\"+f%28x%29+=+ax%5E2+%2B+bx+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum x-value is at:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bmax%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-1+ ALIGN=MIDDLE  ALT=\"+a+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+32+ ALIGN=MIDDLE  ALT=\"+b+=+32+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bmax%5D+=+-32%2F%282%2A%28-1%29%29+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+=+-32%2F%282%2A%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=+x%5Bmax%5D+=+16+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plug this back into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+32+-+x+ ALIGN=MIDDLE  ALT=\"+y+=+32+-+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+=+32+-+16+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+=+32+-+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+=+16+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, for maximum area, the rectangle is 16 x 16<BR>\n" );
document.write( "and the maximum area is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bmax%5D+=+-x%5E2+%2B+32x+ ALIGN=MIDDLE  ALT=\"+A%5Bmax%5D+=+-x%5E2+%2B+32x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bmax%5D+=+-256+%2B+512+ ALIGN=MIDDLE  ALT=\"+A%5Bmax%5D+=+-256+%2B+512+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bmax%5D+=+256+ ALIGN=MIDDLE  ALT=\"+A%5Bmax%5D+=+256+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can see this maximum area from the plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-5%2C+36%2C+-50%2C+360%2C+-x%5E2+%2B+32x+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-5%2C+36%2C+-50%2C+360%2C+-x%5E2+%2B+32x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "( note this is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+ ALIGN=MIDDLE  ALT=\"+A+\"   DISABLED_style= \"max-width:90%; height:auto;\" > plotted with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > )<BR>\n" );
document.write( "Hope this helps </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );