document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189723>Question 189723</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A box has dimensions that have consecutive numbers for its length, width and height, the height having the smallest of the three dimensions. If the length and width are increased by 2 cm and the height is doubled, the volume now becomes 192 cm3 greater than the original box.  What are the dimensions of the original box? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142369 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=142369\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A box has dimensions that have consecutive numbers for its length, width and height, the height having the smallest of the three dimensions. If the length and width are increased by 2 cm and the height is doubled, the volume now becomes 192 cm3 greater than the original box. What are the dimensions of the original box?<BR>\n" );
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document.write( "Let the dimensions be \"x-1\", x, and \"x+1\"<BR>\n" );
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document.write( "Original dimensions:<BR>\n" );
document.write( "height = x-1<BR>\n" );
document.write( "length = x<BR>\n" );
document.write( "width = x+1<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "Original volume is (x-1)*x*(x+1) = x(x^2-1) = x^3-x<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "New dimensions:<BR>\n" );
document.write( "height = 2x-2<BR>\n" );
document.write( "length = x+2<BR>\n" );
document.write( "width = x+3<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "new volumn - old volumn = 19 2cm^3<BR>\n" );
document.write( "2(x-1)(x+2)(x+3) - (x^3-x) = 192<BR>\n" );
document.write( "x = 4<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "height = x-1 = 3<BR>\n" );
document.write( "length = x = 4<BR>\n" );
document.write( "width = x+1 = 5<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
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