document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=766489>Question 766489</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a rectangular piece of cardboard has an area of 15cm2. By cutting a  square 2cm wide on each side from each of the corners and fold up the sides an open box is formed having a volume of 132ml.find the lenght of the original cardboard?<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 #466953 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=466953\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This rectangular board is x by y cm^2, and both lengths are variable.<BR>\n" );
document.write( "The area allows us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=15 ALIGN=MIDDLE  ALT=\"xy=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm^2.  Equivalently, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=15%2Fx ALIGN=MIDDLE  ALT=\"y=15%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Cutting out the corners and folding to make the rectangular space you have height of 2 cm, so  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-2%2A2%29%28y-2%2A2%29=132 ALIGN=MIDDLE  ALT=\"2%28x-2%2A2%29%28y-2%2A2%29=132\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "simplifiable to <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%28y-4%29=66 ALIGN=MIDDLE  ALT=\"%28x-4%29%28y-4%29=66\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And we earlier found a formula for y relating to x using the initial carboard area....\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2A15%2Fx-4x-4%2A15%2Fx%2B16=66 ALIGN=MIDDLE  ALT=\"x%2A15%2Fx-4x-4%2A15%2Fx%2B16=66\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15-4x-60%2Fx%2B16=66 ALIGN=MIDDLE  ALT=\"15-4x-60%2Fx%2B16=66\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x-60%2Fx=66-31 ALIGN=MIDDLE  ALT=\"-4x-60%2Fx=66-31\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x-60%2Fx=35 ALIGN=MIDDLE  ALT=\"-4x-60%2Fx=35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%5E2-60=35x ALIGN=MIDDLE  ALT=\"-4x%5E2-60=35x\"   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=highlight%282x%5E2%2B17.5x%2B30=0%29 ALIGN=MIDDLE  ALT=\"highlight%282x%5E2%2B17.5x%2B30=0%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%284x%5E2%2B35x%2B60=0%29 ALIGN=MIDDLE  ALT=\"highlight%284x%5E2%2B35x%2B60=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "General solution to quadratic equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-35%2B-sqrt%2835%5E2-4%2A4%2A60%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x=%28-35%2B-sqrt%2835%5E2-4%2A4%2A60%29%29%2F%282%2A4%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=%28-35%2B-sqrt%28265%29%29%2F8 ALIGN=MIDDLE  ALT=\"x=%28-35%2B-sqrt%28265%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We want the positive value for x:<BR>\n" );
document.write( "...It's not happening...<BR>\n" );
document.write( "....?\r<BR>\n" );
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document.write( "CONSIDER:<BR>\n" );
document.write( "Taking out a 2 by 2 square at each corner means 4*(2*2) cm^2 removed.  This is 16 cm^2, but you were only given 15 cm^2.  The problem is therefore impossible. </SPAN>\n" );
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