document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1060643>Question 1060643</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An open-topped box can be created by cutting congruent squares from each of the four corners of a piece of cardboard that has dimensions of 20cm by 30cm and folding up the sides. Determine the dimensions of the squares that must be cut to create a box with a volume of 1008cm^3. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #675522 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=675522\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Dimensions x and y<BR>\n" );
document.write( "Uniform sidelength of each square, w<BR>\n" );
document.write( "Volume of box, v\r<BR>\n" );
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document.write( "w is also how high or tall the box.<BR>\n" );
document.write( "Bottom area when flaps folded will be  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2w%29%28y-2w%29 ALIGN=MIDDLE  ALT=\"%28x-2w%29%28y-2w%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "MAIN STARTING EQUATION:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%28x-2w%29%28y-2w%29=v ALIGN=MIDDLE  ALT=\"w%28x-2w%29%28y-2w%29=v\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "STEPS\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%28xy-2yw-2xw%2B4w%5E2%29-v=0 ALIGN=MIDDLE  ALT=\"w%28xy-2yw-2xw%2B4w%5E2%29-v=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xyw-2yw%5E2-2xw%5E2%2B4w%5E3-v=0 ALIGN=MIDDLE  ALT=\"xyw-2yw%5E2-2xw%5E2%2B4w%5E3-v=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4w%5E3-2%28x%2By%29w%5E2%2Bxyw-v=0 ALIGN=MIDDLE  ALT=\"4w%5E3-2%28x%2By%29w%5E2%2Bxyw-v=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-------Cubic equation in the unknown variable, w.\r<BR>\n" );
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document.write( "Make the substitutions and simplify from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=20%2Cy=30%2Cv=1008%29 ALIGN=MIDDLE  ALT=\"system%28x=20%2Cy=30%2Cv=1008%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the equation becomes  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E3-25w%5E2%2B150w-252=0 ALIGN=MIDDLE  ALT=\"w%5E3-25w%5E2%2B150w-252=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "You can try looking for zeros or roots based on Rational Roots theorem.  The practical factorizations which would be useful for the term,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-252 ALIGN=MIDDLE  ALT=\"-252\"   DISABLED_style= \"max-width:90%; height:auto;\" > would be  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=252=2%2A126=3%2A84=4%2A63=6%2A42 ALIGN=MIDDLE  ALT=\"252=2%2A126=3%2A84=4%2A63=6%2A42\"   DISABLED_style= \"max-width:90%; height:auto;\" >; so continue this by testing roots  1, 2, 3, 4, 6, 7, and see if any give remainder of 0 when using synthetic division.\r<BR>\n" );
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document.write( "(3 and 4.92 both will work). </SPAN>\n" );
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