document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=280710>Question 280710</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rick has a rectangular piece of cardboard that is twice as long as it is wide.  From each of the 4 corners, Rick cuts a 2in square and turns up the flaps to form an uncovered box.  If the volume of the box is 896in^3, what were the dimensions of the original piece of cardboard? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #204021 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=204021\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> l = 2w  :: length is twice the width<BR>\n" );
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document.write( "New box dimensions:<BR>\n" );
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document.write( "l-4 = length - 2 corners cut away at 2 inches each<BR>\n" );
document.write( "w - 4 = w - 2 corners cut away at 2 inches each<BR>\n" );
document.write( "(l-4)(w-4)*2 = volume = 896 cubic inches<BR>\n" );
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document.write( "substituting l = 2w<BR>\n" );
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document.write( "(2w-4)(w-4)*2 = 896<BR>\n" );
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document.write( "divide both sides by 2<BR>\n" );
document.write( "(2w-4)(w-4) = 896/2 = 448<BR>\n" );
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document.write( "collect and simplify<BR>\n" );
document.write( "2w^2 -8w -4w +16 - 448 = 0<BR>\n" );
document.write( "2w^2 -12w -432 = 0<BR>\n" );
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document.write( "divide by 2 to further simplify<BR>\n" );
document.write( "w^2 -6w - 216 = 0<BR>\n" );
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document.write( "Thinking about factoring...<BR>\n" );
document.write( "216 = 2*108 = 2*2*54= 2*2*2*27 = 2*2*2*3*9<BR>\n" );
document.write( "2*2*3 = 12<BR>\n" );
document.write( "2*9 = 18<BR>\n" );
document.write( "12 & 18 are 6 apart,\r<BR>\n" );
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document.write( "So the factoring is:<BR>\n" );
document.write( "(w-18)(w+12) = 0<BR>\n" );
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document.write( "Roots are w = 18 and w = -12.<BR>\n" );
document.write( "But negative width is nonsense, so we think w = 18.<BR>\n" );
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document.write( "Substituting in l = 2w<BR>\n" );
document.write( "l = 2*18 = 36<BR>\n" );
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document.write( "Thus we think the original dimensions of the cardboard are length = 36 and width = 18.<BR>\n" );
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document.write( "Checking our work, what is the volume of the box?<BR>\n" );
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document.write( "Recall the volume of the box is based on different dimensions:<BR>\n" );
document.write( "l-4 = 36-4 = 32<BR>\n" );
document.write( "w-4 = 18-4 = 14<BR>\n" );
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document.write( "is the volume of a box 32 by 14 by 2 = 896?<BR>\n" );
document.write( "Yes it is!<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "The original dimensions of the box are length = 36 and width = 18.<BR>\n" );
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document.write( "Done </SPAN>\n" );
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