document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188850>Question 188850</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534400507/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular piece of cardboard is 2 units longer than it is wide.  From each of its corners a square piece 2 units on a side is cut out.  The flaps are then turned up to form an open box that has a volume of 70 cubic units.  Find the length and width of the original piece of cardboard.\r<BR>\n" );
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document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #141619 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=141619\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rectangular piece of cardboard is 2 units longer than it is wide.<BR>\n" );
document.write( " From each of its corners a square piece 2 units on a side is cut out.<BR>\n" );
document.write( " The flaps are then turned up to form an open box that has a volume of 70 cubic units.<BR>\n" );
document.write( " Find the length and width of the original piece of cardboard.<BR>\n" );
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document.write( "Let x = the width of the cardboard<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(x+2) = the length of the cardboard<BR>\n" );
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document.write( "4 units will be subtracted from the length and width<BR>\n" );
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document.write( "Length of the box: (x+2)-4 = (x-2)<BR>\n" );
document.write( "Width of the box = (x-4)<BR>\n" );
document.write( "Height of the box = 2 units<BR>\n" );
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document.write( "Find the area of the bottom of the box<BR>\n" );
document.write( "(x-2)*(x-4) = x^2 - 6x + 8<BR>\n" );
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document.write( "Find the volume (Multiply by the height) given as 70 cu/units<BR>\n" );
document.write( "2(x^2 - 6x + 8) = 70<BR>\n" );
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document.write( "Simplify, divide both sides by 2<BR>\n" );
document.write( "x^2 - 6x + 8 = 35<BR>\n" );
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document.write( "A quadratic equation:<BR>\n" );
document.write( "x^2 - 6x + 8 - 35 = 0<BR>\n" );
document.write( "x^2 - 6x - 27 = 0<BR>\n" );
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document.write( "Factor this to<BR>\n" );
document.write( "(x-9)(x+3) = 0<BR>\n" );
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document.write( "The positive solution is what we want here:<BR>\n" );
document.write( "x = 9 units is the width of the cardboard<BR>\n" );
document.write( "then<BR>\n" );
document.write( "9 + 2 = 11 units is the length<BR>\n" );
document.write( ";<BR>\n" );
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document.write( "Is this true?:<BR>\n" );
document.write( "(9-4)(11-4) * 2 =<BR>\n" );
document.write( "5 * 7 * 2 = 70 cu/units </SPAN>\n" );
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