document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=243200>Question 243200</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A triangle has sides with lengths in centimeters that are consecutive even integers. Find the<BR>\n" );
document.write( "lengths if the perimeter is 186 cm. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #178189 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=178189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Always start with the facts and mathematical properties you know.<BR>\n" );
document.write( "Perimeter of a triangle = sum of sides = a + b + c = 186 (given).<BR>\n" );
document.write( "The lengths of the sides are consecutive EVEN integers: x, y, z.<BR>\n" );
document.write( "But that creates a problem with too many unknowns.<BR>\n" );
document.write( "However, there is a better way to depict three consecutive even integers:<BR>\n" );
document.write( "a = x<BR>\n" );
document.write( "b = x + 2<BR>\n" );
document.write( "c = x + 4<BR>\n" );
document.write( "Then when we solve the equation we can determine if x is even.  If not, there's no solution.<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Substituting for the 3 sides in the perimeter equation, we have:<BR>\n" );
document.write( "x + x+2 + x+4 = 186<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Collecting like terms, we have:<BR>\n" );
document.write( "3x + 6 = 186<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Subtracting 6 from both sides:<BR>\n" );
document.write( "3x = 180<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Dividing both sides by 3:<BR>\n" );
document.write( "x = 60<BR>\n" );
document.write( "So, a = 60.<BR>\n" );
document.write( "...<BR>\n" );
document.write( "x + 2 = 60 + 2 = 62<BR>\n" );
document.write( "So, b = 62<BR>\n" );
document.write( "...<BR>\n" );
document.write( "x + 4 = 60 + 4 = 64<BR>\n" );
document.write( "So, c = 64<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Our proposition is that the 3 sides that are consecutive integers are: 60, 62 & 64.<BR>\n" );
document.write( "We can check by substituting back into the givens.<BR>\n" );
document.write( "Do 60 + 62 + 64 qualify as consecutive even integers. Yes.<BR>\n" );
document.write( "Does 60 + 62 + 64 = 186?  Yes.<BR>\n" );
document.write( "Done. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );