document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1152808>Question 1152808</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a certain rectangular prism, the total length of all the edges is 40 and the total surface area is 48. Find the length of the diagonal connecting one corner to the opposite corner. </SPAN>\n" );
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document.write( "Let the dimensions of the prism be a, b, and c.  Then<br><BR>\n" );
document.write( "(1) The total length of all the edges is 40:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28a%2Bb%2Bc%29+=+40 ALIGN=MIDDLE  ALT=\"4%28a%2Bb%2Bc%29+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" >  -->  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc+=+10 ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(2) The total surface area is 48:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab%2B2ac%2B2bc+=+48 ALIGN=MIDDLE  ALT=\"2ab%2B2ac%2B2bc+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The length we are looking for is the length of the space diagonal of the prism, which is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%5E2%2Bb%5E2%2Bc%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%5E2%2Bb%5E2%2Bc%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Square equation (1) and substitute equation (2):<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%2Bc%29%5E2+=+100+=+a%5E2%2Bb%5E2%2Bc%5E2%2B2ab%2B2ac%2B2bc ALIGN=MIDDLE  ALT=\"%28a%2Bb%2Bc%29%5E2+=+100+=+a%5E2%2Bb%5E2%2Bc%5E2%2B2ab%2B2ac%2B2bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100+=+a%5E2%2Bb%5E2%2Bc%5E2%2B48 ALIGN=MIDDLE  ALT=\"100+=+a%5E2%2Bb%5E2%2Bc%5E2%2B48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2%2Bc%5E2+=+100-48+=+52 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2%2Bc%5E2+=+100-48+=+52\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%5E2%2Bb%5E2%2Bb%5E2%29+=+sqrt%2852%29+=+2sqrt%2813%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%5E2%2Bb%5E2%2Bb%5E2%29+=+sqrt%2852%29+=+2sqrt%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The length of the diagonal is 2*sqrt(13).<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );