document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1003749>Question 1003749</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A box with no top is to be formed from a rectangular cardboard by cutting 4 cm squares from the corners and folding up the sides. The length of the box is to be 2 cm more than its width and its volume is to be 252 cubic cm.\r<BR>\n" );
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document.write( "A.) find the dimensions of the sheet of cardboard.\r<BR>\n" );
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document.write( "B.) find the dimensions of the box. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #620433 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=620433\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A box with no top is to be formed from a rectangular cardboard by cutting 4 cm squares from the corners and folding up the sides.<BR>\n" );
document.write( " The length of the box is to be 2 cm more than its width and its volume is to be 252 cubic cm.<BR>\n" );
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document.write( "A.) find the dimensions of the sheet of cardboard.<BR>\n" );
document.write( "let L = the length of the cardboard<BR>\n" );
document.write( "let w = the width of the card board<BR>\n" );
document.write( "Cutting 4\" corners from the sheet means the height is 4\" and the dimensions are:<BR>\n" );
document.write( "(L-8) = the length of box<BR>\n" );
document.write( "(W-8) = width of the box<BR>\n" );
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document.write( "The volume of the box equation<BR>\n" );
document.write( "(L-8)*(w-8)*4 = 252<BR>\n" );
document.write( "divide both sides by 4<BR>\n" );
document.write( "(L-8)*(w-8) = 63<BR>\n" );
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document.write( "\"The length of the box is to be 2 cm more than its width\"<BR>\n" );
document.write( "L - 8 = w - 8 + 2<BR>\n" );
document.write( "L = w - 8 + 2 + 8<BR>\n" );
document.write( "L = w + 2<BR>\n" );
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document.write( "(L-8)*(w-8) = 63<BR>\n" );
document.write( "Replace L with (w+2)<BR>\n" );
document.write( "((w+2)-8)*(w-8) = 63<BR>\n" );
document.write( "(w-6)(w-8) = 63<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "w^2 - 8w - 6w + 48 = 63<BR>\n" );
document.write( "w^2 - 14w + 48 - 63 = 0<BR>\n" );
document.write( "w^2 - 14w - 15 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(w-15)(s+1) = 0<BR>\n" );
document.write( "The positive solution is all we want here<BR>\n" );
document.write( "w = 15 cm is the width of the sheet of cardboard<BR>\n" );
document.write( "then<BR>\n" );
document.write( "15 + 2 = 17 cm is the length<BR>\n" );
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document.write( "The dimensions of the sheet of cardboard: 17 by 15 cm\r<BR>\n" );
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document.write( "B.) find the dimensions of the box.<BR>\n" );
document.write( "subtract 8 cm from length and width<BR>\n" );
document.write( "9 by 7 by 4 cm is dimensions of the box<BR>\n" );
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document.write( "Check this by finding the volume using these value<BR>\n" );
document.write( "9 * 7 * 4 = 252 cu/cm </SPAN>\n" );
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