document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205301>Question 1205301</A>: <I><SPAN STYLE=\"word-break: break-all;\"> is it possible for a triangle to have sides of 6 inches 12 inches and 17 inches?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842015 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=842015\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Use the <a  rel=nofollow HREF=\"https://www.algebra.com/algebra/homework/Triangles/triangle-inequality-theorem.lesson\">Triangle Inequality Theorem</a> to establish these 3 inequalities:<BR>\n" );
document.write( "a+b > c<BR>\n" );
document.write( "a+c > b<BR>\n" );
document.write( "b+c > a<BR>\n" );
document.write( "If all 3 inequalities are true, then a triangle is possible.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In this case we have: a = 6, b = 12, c = 17.<BR>\n" );
document.write( "<TABLE  border=1 cellpadding=5>\n" );
document.write( "<tr><TD >a+b > c</br>6+12 > 17</br>18 > 17</br><font color=blue>true</font></TD><TD >a+c > b</br>6+17 > 12</br>23 > 12</br><font color=blue>true</font></TD><TD >b+c > a</br>12+17 > 6</br>29 > 6</br><font color=blue>true</font></TD></tr>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<font color=blue>All 3</font> inequalities are <font color=blue>true</font>, so a <font color=blue size=4>triangle is possible</font> when the sides are 6 inches, 12 inches, and 17 inches.<BR>\n" );
document.write( "Adding any two sides produces a sum larger than the third side.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.geogebra.org/calculator\">GeoGebra</a> can be used to confirm the answer. <BR>\n" );
document.write( "Alternatively you can use slips of paper, or pieces of string, to try it out yourself. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Another example: <BR>\n" );
document.write( "Is a triangle possible when a = 2, b = 3, c = 10?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  border=1 cellpadding=5>\n" );
document.write( "<tr><TD >a+b > c</br>2+3 > 10</br>5 > 10</br><font color=red>false</font></TD><TD >a+c > b</br>2+10 > 3</br>12 > 3</br><font color=blue>true</font></TD><TD >b+c > a</br>3+10 > 2</br>13 > 2</br><font color=blue>true</font></TD></tr>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "The 1st inequality being <font color=red>false</font> means a triangle is <font color=red>not possible</font> when the sides are 2, 3, and 10.<BR>\n" );
document.write( "We have 2 inequalities that are true, but we need ALL 3 of them to be true.<BR>\n" );
document.write( "Technically you do not have to check the other inequalities once you reach a false inequality. But it could be good practice.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );