document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=259834>Question 259834</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A box with rectangular sides has width twice the length of the base. The volume is 24 cubic inches and the total surface area of all six sides is 52 square inches. Write down a (cubic) equation whose solution is the length of the box. \r<BR>\n" );
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document.write( "Use L for the length of the box.<BR>\n" );
document.write( "Equation: 0 =\r<BR>\n" );
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document.write( "I know the base would be L2 and the sides would be 2L*L and since there are 2 bases it would be 2(2L) and four sides 4(2L^2), but I do not really know where to go from there. Any help would be great, thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #191306 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=191306\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let \r<BR>\n" );
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document.write( "L = Length, W = Width, H = Height\r<BR>\n" );
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document.write( "Recall that the formula for the volume of the box is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=LWH ALIGN=MIDDLE  ALT=\"V=LWH\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie multiply the length, width, and height to find the volume)\r<BR>\n" );
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document.write( "In addition, the surface area is simply the sum of the individual areas of the 6 faces on the box. Since there are essentially 2 of each face, we have the basic surface area formula \r<BR>\n" );
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document.write( "Surface Area = 2*Length*Width+2*Width*Height+2*Length*Height\r<BR>\n" );
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document.write( "which can be rewritten as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=2LW%2B2WH%2B2LH ALIGN=MIDDLE  ALT=\"S=2LW%2B2WH%2B2LH\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now because \"A box with rectangular sides has width twice the length of the base\", we can say that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=2L ALIGN=MIDDLE  ALT=\"W=2L\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie double the length to get the width)\r<BR>\n" );
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document.write( "So for each equation above, we can plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=2L ALIGN=MIDDLE  ALT=\"W=2L\"   DISABLED_style= \"max-width:90%; height:auto;\" > to eliminate W altogether. What will result will be two equations with two unknowns (which is now possible to solve, if there is a solution).\r<BR>\n" );
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document.write( "So plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=2L ALIGN=MIDDLE  ALT=\"W=2L\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=LWH ALIGN=MIDDLE  ALT=\"V=LWH\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=2L%5E2H ALIGN=MIDDLE  ALT=\"V=2L%5E2H\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Also, plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=24 ALIGN=MIDDLE  ALT=\"V=24\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the given volume) to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24=2L%5E2H ALIGN=MIDDLE  ALT=\"24=2L%5E2H\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This will be equation 1.\r<BR>\n" );
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document.write( "Now plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=2L ALIGN=MIDDLE  ALT=\"W=2L\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=2LW%2B2WH%2B2LH ALIGN=MIDDLE  ALT=\"S=2LW%2B2WH%2B2LH\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=4L%5E2%2B4LH%2B2LH ALIGN=MIDDLE  ALT=\"S=4L%5E2%2B4LH%2B2LH\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Also, plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=52 ALIGN=MIDDLE  ALT=\"S=52\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the given surface area) to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52=4L%5E2%2B4LH%2B2LH ALIGN=MIDDLE  ALT=\"52=4L%5E2%2B4LH%2B2LH\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We'll refer to this as equation 2.\r<BR>\n" );
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document.write( "So you should now have the system of equations\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2824=2L%5E2H%2C52=4L%5E2%2B4LH%2B2LH%29 ALIGN=MIDDLE  ALT=\"system%2824=2L%5E2H%2C52=4L%5E2%2B4LH%2B2LH%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To solve this system, simply isolate one variable and use substitution. I'll let you finish the problem. Let me know if you still need help. </SPAN>\n" );
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