document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1003752>Question 1003752</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a box with no top is to be formed from a rectangular cardboard by cutting 4cm squares from the corners and folding up the sides. the length of the box is to be 2cm more than its width and its volume is to be 252 cubic cm. find the dimensions of the sheet of the cardboard </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #620413 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=620413\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> volume = length * width * height\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "volume = 252\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "length * width * height = 252\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your height will be 4 cm because you are cutting our 4 cm squares from each end and then folding up what is left.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your width is assumed to be x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if your width is x, then your length has to be x + 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "length * width * height = 252 becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x + 2) * x * 4 = 252\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of this equation by 4 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x + 2) * x = 63\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^2 + 2x = 63\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 63 from both sides of this equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^2 + 2x - 63 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "factor this quadratic equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x + 9) * (x - 7) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for x to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = -9 or x = 7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x can't be negative, so you are left with x = 7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's the width.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the length is equal to 2 + 2 which is equal to 9.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your box will have dimensions of:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "length = 9<BR>\n" );
document.write( "width = 7<BR>\n" );
document.write( "height = 4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now you have to figure out what size paper you will need.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the length of your paper will have to be 9 cm + 4 cm on each end = 9 cm + 8 cm = 17 cm.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the width of your paper will have to be 7 cm + 4 cm on each end = 7 cm + 8 cm = 15 cm.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your paper will have to be 17 cm by 15 cm.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a picture of what your paper will look like after you marked it for cutting is shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/111501.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );