document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181832>Question 1181832</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular box has a volume of 200cm^3.<BR>\n" );
document.write( "(a) find three possible whole number sets of dimensions that give the correct volume\r<BR>\n" );
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document.write( "(b) Find three sets of dimensions with at least one non-whole number that give the correct volume. \r<BR>\n" );
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document.write( "okay so for (a) I'm experienced enough to get all three sets in my head: 5*4*10, 2*10*10 and 20*2*5, which all equal to 200cm cube.\r<BR>\n" );
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document.write( "but for (b) how can I find non-whole numbers like decimals as the dimensions, are there any reliable algebraic calculations for this?\r<BR>\n" );
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document.write( "My Ideas:<BR>\n" );
document.write( "So for a decimal number right, its a whatever number divide by 10 or 10 to the power of something. So for example to find a decimal number we can randomly generate a number 825 in our brain. To make this number a decimal, we divide it by 10 which equals 82.5 or we can divide by another 10 which = 8.25. Okay, with this knowledge I create these equations n = a/10 and a/10 * b * h = 200. But the things is b and h can be anything we want. So I tried a/10 * 4 * 8 = 200, a = 62.5, therefore 6.25 is the non-whole number I need.<BR>\n" );
document.write( " But I realize there is a flaw in my way, because if I try 4 and 2 as b and h, then a/10*4*2=200<BR>\n" );
document.write( "a = 250<BR>\n" );
document.write( "which makes my number n = 250/10 = 25 which is still a whole number. Do I just use trial and error on (b and h) until I get my non-whole number or are there different ways?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #811746 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=811746\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "the volume of a rectangular box is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=a%2Ab%2Ah ALIGN=MIDDLE  ALT=\"V=a%2Ab%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(a) find three possible whole number sets of dimensions that give the correct volume\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200=2%5E3%2A5%5E2 ALIGN=MIDDLE  ALT=\"200=2%5E3%2A5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > prime factors, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+ ALIGN=MIDDLE  ALT=\"2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >distinct)\r<BR>\n" );
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document.write( "choose three:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=5cm ALIGN=MIDDLE  ALT=\"a=5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5cm ALIGN=MIDDLE  ALT=\"b=5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=8cm ALIGN=MIDDLE  ALT=\"h=8cm\"   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=V=5cm%2A5cm%2A8cm ALIGN=MIDDLE  ALT=\"V=5cm%2A5cm%2A8cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=200cm%5E3 ALIGN=MIDDLE  ALT=\"V=200cm%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(b) Find three sets of dimensions with at least one non-whole number that give the correct volume.\r<BR>\n" );
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document.write( "write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E3 ALIGN=MIDDLE  ALT=\"2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2F5%29%2A5=1.6%2A5 ALIGN=MIDDLE  ALT=\"%288%2F5%29%2A5=1.6%2A5\"   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=a=1.6cm ALIGN=MIDDLE  ALT=\"a=1.6cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5cm ALIGN=MIDDLE  ALT=\"b=5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=25cm ALIGN=MIDDLE  ALT=\"h=25cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=1.6cm%2A5cm%2A25cm ALIGN=MIDDLE  ALT=\"V=1.6cm%2A5cm%2A25cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=200cm%5E3 ALIGN=MIDDLE  ALT=\"V=200cm%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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