document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1078873>Question 1078873</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rick has 45 cubes each with a side length of 1cm.  He wants to use all his cubes to make a cuboid that has a square base.  His friend suggests 1cm X 1cm  and a height of 45cm.  Find the dimensions of a different cuboid he could use from all his cubes. It should have a square base.  <BR>\n" );
document.write( "The answer states base 2x5 With a height of 9cm.  Saying you must have 1 square number and 2 primes so 2x5x9=90. Where does the 90 comes from ?  It says a base of 2x9 but that's not square. With a heigh of 9cm. Can anyone help?  Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #693270 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=693270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> one reference on cuboids:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.mathsisfun.com/geometry/cuboids-rectangular-prisms.html\" target = \"_blank\">https://www.mathsisfun.com/geometry/cuboids-rectangular-prisms.html</a>\r<BR>\n" );
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document.write( "you have 45 cubes, each with a side length of 1 cm.\r<BR>\n" );
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document.write( "you want a cuboid with a square base.\r<BR>\n" );
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document.write( "1 cube as the base and 45 cubes as the height will do.\r<BR>\n" );
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document.write( "basically, you want to divide the number of cubes total by the number of cubes as the base.\r<BR>\n" );
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document.write( "if you get an even number, then that's good.\r<BR>\n" );
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document.write( "if you can't, then that's no good.\r<BR>\n" );
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document.write( "1 cube as the base give you 45 cubes as the height so that's ok.\r<BR>\n" );
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document.write( "next size base could be 2 by 2, but that would take 4 cubes and 45 / 4 is not even.\r<BR>\n" );
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document.write( "next size base could be 3 by 3, but that would take 9 cubes and 45 / 9 = 5.\r<BR>\n" );
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document.write( "that looks like it'll work.\r<BR>\n" );
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document.write( "the dimensions would be 3 by 3 by 5 for a total of 45 square cm.\r<BR>\n" );
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document.write( "i believe the answer given in the book is wrong.\r<BR>\n" );
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document.write( "2 by 5 by 9 would result in total square cm of 90 which is not right.\r<BR>\n" );
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document.write( "that would use 90 squares, as you say.\r<BR>\n" );
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document.write( "not only that, the base would not be square.\r<BR>\n" );
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document.write( "keep in mind the book is not always right.\r<BR>\n" );
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document.write( "some books are better than others.\r<BR>\n" );
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document.write( "the best have very few to no errors.\r<BR>\n" );
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document.write( "the worst?\r<BR>\n" );
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document.write( "some are really bad.\r<BR>\n" );
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document.write( "the problems can stem anywhere from the person or persons who wrote the book to the translation of the original problems to the final form.\r<BR>\n" );
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document.write( "the problems can be human or technical or both, sometimes just a typo is enough to throw it off.\r<BR>\n" );
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document.write( "a general rule that i would use is to find the possible square bases first and then divide 45 by the number of cubes used in the base.\r<BR>\n" );
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document.write( "if the number divides evenly, then you have your cuboid.\r<BR>\n" );
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document.write( "the height is determined by stacking up the cubes used in the base on top of each other.\r<BR>\n" );
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document.write( "base of 1 by 1 requires 1 cube divides into 45 evenly.<BR>\n" );
document.write( "height is 45 because 45 times the base of 1 cube requires 45 cubes.\r<BR>\n" );
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document.write( "base of 2 by 2 requires 4 cubes does not divide into 45 evenly.\r<BR>\n" );
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document.write( "base of 3 by 3 requires 9 cubes divides into 45 evenly.<BR>\n" );
document.write( "height is 5 because 5 times the base of 9 cubes requires 45 cubes.\r<BR>\n" );
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document.write( "base of 4 by 4 requires 16 cubes does not divide into 45 evenly.\r<BR>\n" );
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document.write( "base of 5 by 5 requires 25 cubes does not divide into 45 evenly.\r<BR>\n" );
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document.write( "base of 6 by 6 requires 36 cubes does not divide into 45 evenly.\r<BR>\n" );
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document.write( "base of 7 by 7 requires 49 cubes which is greater than 45 so you're out of possible choices for the base.\r<BR>\n" );
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document.write( "the only bases that work are 1 by 1 and 3 by 3.\r<BR>\n" );
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