document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205187>Question 1205187</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A triangle has one side that is 8\" and another side that is 13\". What I'd the minimum length of the third side? What is the maximum length of the third side? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841829 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=841829\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll be using the Triangle Inequality Theorem.<BR>\n" );
document.write( "More info is found here<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.algebra.com/algebra/homework/Triangles/triangle-inequality-theorem.lesson\">https://www.algebra.com/algebra/homework/Triangles/triangle-inequality-theorem.lesson</a><BR>\n" );
document.write( "Specifically I'll use the extension of that theorem mentioned after example 2.\r<BR>\n" );
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document.write( "If we know two sides of a triangle a and b, then possible values for the third side c is found through the inequality:<BR>\n" );
document.write( "b-a < c < b+a<BR>\n" );
document.write( "where b > a\r<BR>\n" );
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document.write( "In this case<BR>\n" );
document.write( "a = 8<BR>\n" );
document.write( "b = 13<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "b-a < c < b+a<BR>\n" );
document.write( "13-8 < c < 13+8<BR>\n" );
document.write( "5 < c < 21\r<BR>\n" );
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document.write( "Side c is between 5 inches and 21 inches, excluding both endpoints.<BR>\n" );
document.write( "Something like c = 5.1 is valid, but c = 5 is not.<BR>\n" );
document.write( "Technically there is no smallest value for c because we could have the following<BR>\n" );
document.write( "c = 5.1<BR>\n" );
document.write( "c = 5.01<BR>\n" );
document.write( "c = 5.001<BR>\n" );
document.write( "c = 5.0001<BR>\n" );
document.write( "and so on<BR>\n" );
document.write( "We can approach 5 but not actually arrive there.\r<BR>\n" );
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document.write( "If we limit c to just the integers, then c = 6 would be the smallest side possible.<BR>\n" );
document.write( "Otherwise, there is no smallest value.\r<BR>\n" );
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document.write( "The same can be said about the other end of the spectrum as well. <BR>\n" );
document.write( "There is no largest value if c is a real number (since we could have c = 20.9 or c = 20.99 or c = 20.999 and so on). <BR>\n" );
document.write( "But if c was an integer, then c = 20 is the largest possible.<BR>\n" );
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