document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1067836>Question 1067836</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the sum of length, breadth and depth of a cuboid is 19 cm and the length of diagonal is 11 cm. find the surface area of the cuboid. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #683024 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=683024\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the length, breadth and depth of the cuboid.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz=19 ALIGN=MIDDLE  ALT=\"x%2By%2Bz=19\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%2By%5E2%2Bz%5E2%29=11 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%2By%5E2%2Bz%5E2%29=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2Bz%5E2=121 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2Bz%5E2=121\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "are out clues, <BR>\n" );
document.write( "and of course <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%3E0%2Cy%3E0%2Cz%3E0%29 ALIGN=MIDDLE  ALT=\"system%28x%3E0%2Cy%3E0%2Cz%3E0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%2Bz%29%5E2=19%5E2 ALIGN=MIDDLE  ALT=\"%28x%2By%2Bz%29%5E2=19%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2Bz%5E2%2B2%28x%2By%2Bz%29=361 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2Bz%5E2%2B2%28x%2By%2Bz%29=361\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%5E2%2By%5E2%2Bz%5E2%2B2%28x%2By%2Bz%29=361%2Cx%5E2%2By%5E2%2Bz%5E2=121%29 ALIGN=MIDDLE  ALT=\"system%28x%5E2%2By%5E2%2Bz%5E2%2B2%28x%2By%2Bz%29=361%2Cx%5E2%2By%5E2%2Bz%5E2=121%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22%28x%2By%2Bz%29=361-121=highlight%28240%29 ALIGN=MIDDLE  ALT=\"22%28x%2By%2Bz%29=361-121=highlight%28240%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "and yes, there are other options beyond {x,y,z} = {6,6,7} ,<BR>\n" );
document.write( "but none with three integers, and the options fall in a narrow range.around <BR>\n" );
document.write( "You can make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=19-x-y ALIGN=MIDDLE  ALT=\"z=19-x-y\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "substitute into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2Bz%5E2=121 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2Bz%5E2=121\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to get an equation of degree 2 in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For the equation to have a solution for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "you need <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2F3%3Cx%3C7 ALIGN=MIDDLE  ALT=\"17%2F3%3Cx%3C7\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "To figure out if there would be another solution with integers,<BR>\n" );
document.write( "I searched on line for \"Pythagorean quadruples\",<BR>\n" );
document.write( "sets of 4 whole numbers, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C7%2Ca%2C%22%2C%22%2Cb%2C%22%2C%22%2Cc%2C%22%2C%22%2Cd%29 ALIGN=MIDDLE  ALT=\"matrix%281%2C7%2Ca%2C%22%2C%22%2Cb%2C%22%2C%22%2Cc%2C%22%2C%22%2Cd%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2%2Bc%5E2=d%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2%2Bc%5E2=d%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The lists are given with the numbers <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C7%2Ca%2C%22%2C%22%2Cb%2C%22%2C%22%2Cc%2C%22%2C%22%2Cd%29 ALIGN=MIDDLE  ALT=\"matrix%281%2C7%2Ca%2C%22%2C%22%2Cb%2C%22%2C%22%2Cc%2C%22%2C%22%2Cd%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "in such order that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3C=b%3C=c%3Cd ALIGN=MIDDLE  ALT=\"a%3C=b%3C=c%3Cd\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so you only have to the first few<BR>\n" );
document.write( "to realize that the only two ending in 11 are<BR>\n" );
document.write( "2, 6, 9, 11 and 6, 6, 7, 11 . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );