document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=283621>Question 283621</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The ratio of the dimensions of a rectangular solid is 5:4:3, and the ratio of this solid's volume to its surface area is 2:1.  What is the length of the solid's shortest side? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #205837 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=205837\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sides of of rectangular solid are  (LWH) in proportion 5:4:3<BR>\n" );
document.write( "We don't know which sides are which.<BR>\n" );
document.write( "volume =L*H*W<BR>\n" );
document.write( "There are six surface areas. Two of each<BR>\n" );
document.write( "LW+LW+HW+HW+LH+LH<BR>\n" );
document.write( "2LW+2HW+2LH<BR>\n" );
document.write( "5x=L<BR>\n" );
document.write( "4x=W<BR>\n" );
document.write( "3x=H\r<BR>\n" );
document.write( "\n" );
document.write( "A=2*(LW+HW+LH)<BR>\n" );
document.write( "V =LWH<BR>\n" );
document.write( "V/A=2/1\r<BR>\n" );
document.write( "\n" );
document.write( " 5x=L,4x=W,3x=H,  (L*W*H)/(2*(L*W+H*W+L*H))=2/1<BR>\n" );
document.write( "H = 47/5,   L = 47/3,   W = 188/15,   x = 47/15<BR>\n" );
document.write( "H=9.4,   L=15.6667,   W=12.5333,   x=3.13333<BR>\n" );
document.write( "188/15 or 9.4 is the shortest side </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );