document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998615>Question 998615</A>: <I><SPAN STYLE=\"word-break: break-all;\">  If each of side of a  triangle has a different lengths, and the lengths of two sides are 7 & 12, the perimeter of this triangle would be...<BR>\n" );
document.write( "A. 31<BR>\n" );
document.write( "B. 26<BR>\n" );
document.write( "C. 25<BR>\n" );
document.write( "D. 23<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616378 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=616378\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = length of third side\r<BR>\n" );
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document.write( "\"the lengths of two sides are 7 & 12\" so\r<BR>\n" );
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document.write( "12-7 < x < 12+7<BR>\n" );
document.write( "5 < x < 19\r<BR>\n" );
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document.write( "If x is the third side, then the third side is between 5 and 19 units (excluding the endpoints).\r<BR>\n" );
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document.write( "So x is somewhere between 5 and 19. The value of x is NOT equal to 5. It is NOT equal to 19.\r<BR>\n" );
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document.write( "We also cannot have x equal to 7 or 12. Why? Because the instructions say that each side is of a different length.\r<BR>\n" );
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document.write( "Notice how if the third side was x = 7, then <BR>\n" );
document.write( "x+7+12 = 7+7+12 = 26<BR>\n" );
document.write( "So choice B is out because again the three sides are different lengths.\r<BR>\n" );
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document.write( "If x = 12, then<BR>\n" );
document.write( "x+7+12 = 12+7+12 = 31<BR>\n" );
document.write( "ruling out choice A\r<BR>\n" );
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document.write( "So we have choice C and choice D left over.\r<BR>\n" );
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document.write( "Focus on 5 < x < 19\r<BR>\n" );
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document.write( "Add 7 to all sides\r<BR>\n" );
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document.write( "5+7 < x+7 < 19+7<BR>\n" );
document.write( "12 < x+7 < 26\r<BR>\n" );
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document.write( "Now add 12 to all sides\r<BR>\n" );
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document.write( "12 < x+7 < 26<BR>\n" );
document.write( "12+12 < x+7+12 < 26+12<BR>\n" );
document.write( "24 < x+7+12 < 38\r<BR>\n" );
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document.write( "The quantity \"x+7+12\" represents the perimeter because it's the sum of the three sides of the triangle. The perimeter is between 24 and 38 (excluding the endpoints)\r<BR>\n" );
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document.write( "As we can see in the inequality 24 < x+7+12 < 38, the perimeter is some number between 24 and 38. So it is impossible for the perimeter to be 23 because it's not in that interval. So choice D is ruled out\r<BR>\n" );
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document.write( "The only thing left is choice C and this is possible when x = 6<BR>\n" );
document.write( "P = x+7+12 = 6+7+12 = 25\r<BR>\n" );
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document.write( "Final Answer: Choice C) 25 </SPAN>\n" );
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