document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183488>Question 1183488</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A square base box has a volume of 200cm, find the dimensions if the height is 3cm more than the length </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813832 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=813832\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The dimensions of the box are x, x, and x+3; the volume is 200.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%28x%29%28x%29%28x%2B3%29+=+x%5E3%2B3x+=+200 ALIGN=MIDDLE  ALT=\"V+=+%28x%29%28x%29%28x%2B3%29+=+x%5E3%2B3x+=+200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "There are no easy ways to solve that cubic equation algebraically; so let's solve the problem informally.<br><BR>\n" );
document.write( "The volume is given to be (EXACTLY) 200.  That means the dimensions of the box are almost certainly whole numbers.<br><BR>\n" );
document.write( "So look at the prime factorization of 200 and find a way to group the factors so that they match the pattern x, x, and x+3.<br><BR>\n" );
document.write( "200 = 2*2*2*5*5 = 5*5*(2*2*2) = 5*5*8 = (x)(x)(x+3)<br><BR>\n" );
document.write( "ANSWER: x=5; the dimensions of the box are x, x, and x+3, which is 5, 5, and 8.<br><BR>\n" );
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