document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=695021>Question 695021</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The volume of a rectangular solid is 540 cubit feet. The width is 3 feet more than the height, and the lenght is 4 more feet than the height. Find the dimensions of the solid.<BR>\n" );
document.write( "w=h+3<BR>\n" );
document.write( "l=h+4<BR>\n" );
document.write( "h= ?<BR>\n" );
document.write( "540=(h+3)*(h+4)*h<BR>\n" );
document.write( "540=h^3+7h^2+12h<BR>\n" );
document.write( "How to resolve ?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #428320 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=428320\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=540=h%5E3%2B7h%5E2%2B12h ALIGN=MIDDLE  ALT=\"540=h%5E3%2B7h%5E2%2B12h\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E3%2B7h%5E2%2B12h-540=0 ALIGN=MIDDLE  ALT=\"h%5E3%2B7h%5E2%2B12h-540=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Any rational zero of the polynomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28h%29=h%5E3%2B7h%5E2%2B12h-540 ALIGN=MIDDLE  ALT=\"P%28h%29=h%5E3%2B7h%5E2%2B12h-540\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be a factor of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=540 ALIGN=MIDDLE  ALT=\"540\"   DISABLED_style= \"max-width:90%; height:auto;\" >, with a + or a - sign.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=540=2%5E2%2A3%5E3%2A5 ALIGN=MIDDLE  ALT=\"540=2%5E2%2A3%5E3%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You know we are looking for a positive solution, so I would try + signs first.<BR>\n" );
document.write( "The choices for factors are 1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270, and 540.<BR>\n" );
document.write( "It is obvious that for positive <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > values, as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > increases, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28h%29 ALIGN=MIDDLE  ALT=\"P%28h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > increases.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%281%29=1%2B7%2B12-540%3C0 ALIGN=MIDDLE  ALT=\"P%281%29=1%2B7%2B12-540%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2810%29=1000%2B700%2B120-540%3E0 ALIGN=MIDDLE  ALT=\"P%2810%29=1000%2B700%2B120-540%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "so the solution could be one of the factors in between 1 and 10: 2,3,4,5,6,and 9.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%285%29=125%2B7%2A25%2B12%2A5-540=125%2B175%2B60-540=360-540=-180 ALIGN=MIDDLE  ALT=\"P%285%29=125%2B7%2A25%2B12%2A5-540=125%2B175%2B60-540=360-540=-180\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "so we expect that the solution could be one of the factors between 5 and 10 (either 6 or 9).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%286%29=216%2B7%2A36%2B12%2A6-540=216%2B252%2B72-540=0 ALIGN=MIDDLE  ALT=\"P%286%29=216%2B7%2A36%2B12%2A6-540=216%2B252%2B72-540=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28h=6%29 ALIGN=MIDDLE  ALT=\"highlight%28h=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is one solution.<BR>\n" );
document.write( "Is there another solution?<BR>\n" );
document.write( "Of course not.<BR>\n" );
document.write( "If we make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > smaller, the width and length will be smaller, and the volume will have to be smaller.<BR>\n" );
document.write( "If we make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > larger, the width and length will be larger, and the volume will have to be larger. </SPAN>\n" );
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