document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=491280>Question 491280</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The longest side of a triangle is 16 less than the sum of the other two. The shortest side is three times the difference of the other two. The Perimeter is 150. Write the system of equation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #334582 by </B><A HREF=/tutors/aboutme.mpl?userid=cleomenius><B>cleomenius(959)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=cleomenius><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=cleomenius><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=334582\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let<BR>\n" );
document.write( "a = longest<BR>\n" );
document.write( "b = middle<BR>\n" );
document.write( "c = smallest<BR>\n" );
document.write( "=========================================================<BR>\n" );
document.write( "Set up our equations.<BR>\n" );
document.write( "-a +b + c =  16<BR>\n" );
document.write( "3a - 3b -c = 0<BR>\n" );
document.write( "a + b + c = 150<BR>\n" );
document.write( "=======================================================<BR>\n" );
document.write( "multiply 1 * 3;add 1 to 2<BR>\n" );
document.write( "-a +b + c =  16<BR>\n" );
document.write( "      2c = 48<BR>\n" );
document.write( "a + b + c = 150<BR>\n" );
document.write( "c = 24 <BR>\n" );
document.write( "=============================================<BR>\n" );
document.write( "plug c into 1 and 3, <BR>\n" );
document.write( "-a +b + 24=  16<BR>\n" );
document.write( "      2c = 48<BR>\n" );
document.write( "a + b + 24= 150<BR>\n" );
document.write( "multiply 1 by -1, add 1 to 3<BR>\n" );
document.write( "-a +b + 24=  16<BR>\n" );
document.write( "      2c = 48<BR>\n" );
document.write( " 2a +  0= 134<BR>\n" );
document.write( "a = 67 degrees.<BR>\n" );
document.write( "========================================================<BR>\n" );
document.write( "Solve for b.<BR>\n" );
document.write( "67 + 24 = 91 ; 150 - 91 = 59<BR>\n" );
document.write( "b = 59 degrees.<BR>\n" );
document.write( "=======================================================<BR>\n" );
document.write( "a = 67 degrees.<BR>\n" );
document.write( "b = 59 degrees.<BR>\n" );
document.write( "c = 24 degrees.<BR>\n" );
document.write( "Now, to check the system.<BR>\n" );
document.write( "59 + 24 = 83; 83 - 16 = 67.<BR>\n" );
document.write( "67 - 59 = 8; 8*3 = 24, which is the smallest angle.<BR>\n" );
document.write( "67 + 59 + 24 = 150. <BR>\n" );
document.write( "This system does check.<BR>\n" );
document.write( "Cleomenius.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );