document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1075200>Question 1075200</A>: <I><SPAN STYLE=\"word-break: break-all;\">  The corners of a piece of paper are cut to make an open top box.  The cut corners are 0.5 in by 0.5 in.  If the width of the paper is two-thirds the height what, what are the dimensions of the paper if the volume is to be 60 cubic inches?    </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #689884 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=689884\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The corners of a piece of paper are cut to make an open top box. The cut corners are 0.5 in by 0.5 in. If the width of the paper is two-thirds the height what, what are the dimensions of the paper if the volume is to be 60 cubic inches? <BR>\n" );
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document.write( "width = (2/3)h inches<BR>\n" );
document.write( "height = h inches<BR>\n" );
document.write( "------<BR>\n" );
document.write( "After cutting the corners::<BR>\n" );
document.write( "width = (2/3)h - 1 inches<BR>\n" );
document.write( "height = h - 1 inches<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Volume Equation:<BR>\n" );
document.write( "h(h-1)((2/3)h-1) = 60 cu in<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "h((2/3)h^2 - (5/3)h + 1) = 60<BR>\n" );
document.write( "---<BR>\n" );
document.write( "(2/3)h^3 - (5/3)h^2 + h - 60 = 0<BR>\n" );
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document.write( "Take the derivative::<BR>\n" );
document.write( "V'(h) = 2h^2 - (10/3)h + 1 <BR>\n" );
document.write( "----<BR>\n" );
document.write( "Solve V'(h) = 0<BR>\n" );
document.write( "h = 1.274 inches (height of the paper)<BR>\n" );
document.write( "(2/3)h = 0.523 inches (width of the paper)<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "-------------- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );