document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=926073>Question 926073</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If DE = 37 cm and EF = 14 cm, then what are the possible lengths for DF so that line DE, line EF, and line DF can form a triangle? Explain your reasoning. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #562049 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=562049\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = length of missing side\r<BR>\n" );
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document.write( "it turns out that if you have a triangle with sides a,b,c with c being the missing side, then c is going to make the following true:\r<BR>\n" );
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document.write( "a-b < c < a+b\r<BR>\n" );
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document.write( "Note: this implies that a >= b\r<BR>\n" );
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document.write( "in this case, x = c, a = 37 and b = 14, so...\r<BR>\n" );
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document.write( "a-b < c < a+b\r<BR>\n" );
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document.write( "37-14 < x < 37+14\r<BR>\n" );
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document.write( "23 < x < 51\r<BR>\n" );
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document.write( "Final Answer:\r<BR>\n" );
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document.write( "The possible lengths for DF are any length between 23 and 51. You do NOT include 23 and you do NOT include 51.\r<BR>\n" );
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document.write( "Jim\r<BR>\n" );
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