document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=739455>Question 739455</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You cut square corners from a piece of cardboard that has dimensions 32 cm by 40 cm. You then fold the cardboard to create a box with no lid. To the nearest centimeter, what are the dimensions of the box that will have the greatest volume?\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #451131 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39630)</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=451131\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> volume, v = area of bottom multiplied by height of each side.\r<BR>\n" );
document.write( "\n" );
document.write( "x=height of each side, from cutting out the corners.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "two sides are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32-2x ALIGN=MIDDLE  ALT=\"32-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and other two sides are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40-2x ALIGN=MIDDLE  ALT=\"40-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > lengths.<BR>\n" );
document.write( "They make the bottom area.  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "v = height * oneSideLength * otherSideLength<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=x%2832-2x%29%2840-2x%29 ALIGN=MIDDLE  ALT=\"v=x%2832-2x%29%2840-2x%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%28v=4x%2816-x%29%2820-x%29%29 ALIGN=MIDDLE  ALT=\"highlight%28v=4x%2816-x%29%2820-x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OR<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28v=4x%5E3-144x%5E2%2B1280x%29 ALIGN=MIDDLE  ALT=\"highlight%28v=4x%5E3-144x%5E2%2B1280x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You would either use a graphing calculator to find the maximum, or resort to Calculus taking derivative to find the maximum.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dv%2Fdx+=+12x%5E2-288x%2B1280+ ALIGN=MIDDLE  ALT=\"dv%2Fdx+=+12x%5E2-288x%2B1280+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%5E2-288x%2B1280+=0 ALIGN=MIDDLE  ALT=\"12x%5E2-288x%2B1280+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );