document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136737>Question 1136737</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the first side of the triangle is 4 cm longer than the second side. the third side is 3 times the second side. The perimeter is 44cm. how long is each side </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754582 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52803)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=754582\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "The tutor @Boreal correctly determined the side lengths from the condition: they are 8 cm, 12 cm and 24 cm.\r<BR>\n" );
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document.write( "But he missed to check, if such a triangle may exist.\r<BR>\n" );
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document.write( "Actually (and factually), there is NO triangle with such side lengths, since it contradicts to the triangle inequality\r<BR>\n" );
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document.write( "    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;a + b > c\r<BR>\n" );
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document.write( "which must be true for any combination of sides of any triangle.\r<BR>\n" );
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document.write( "In our case \r<BR>\n" );
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document.write( "    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;8 + 12 = 20 < 24\r<BR>\n" );
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document.write( "and the triangle inequality fails.\r<BR>\n" );
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document.write( "It is a simple rule, and I repeated it many times in my posts to this forum:\r<BR>\n" );
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document.write( "    when you solve a problem, where you need to determine the side lengths of a triangle,\r\n" );
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document.write( "    you MUST check at the end of your solution, whether the triangle inequalities are satisfied.\r\n" );
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document.write( "    Without doing it, you can make a HUGE mistake.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "It is the major lesson to learn from my post.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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