document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200226>Question 1200226</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Benjamin is drawing a triangle <BR>\n" );
document.write( "and knows that two sides are <BR>\n" );
document.write( "9 centimeters and 12 centimeters. <BR>\n" );
document.write( "What could the third side length be? <BR>\n" );
document.write( "Select all that apply<BR>\n" );
document.write( "2 cm<BR>\n" );
document.write( "4 cm<BR>\n" );
document.write( "10 cm<BR>\n" );
document.write( "18 cm<BR>\n" );
document.write( "21 cm </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834292 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=834292\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answers:<BR>\n" );
document.write( "<font color=red size=4>4 cm<BR>\n" );
document.write( "10 cm<BR>\n" );
document.write( "18 cm</font>\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "We have a triangle with sides a,b, and c.\r<BR>\n" );
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document.write( "a = 9 and b = 12 are the two known sides.<BR>\n" );
document.write( "c is the unknown side.\r<BR>\n" );
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document.write( "Due to the <a  rel=nofollow HREF= \"https://www.mathsisfun.com/geometry/triangle-inequality-theorem.html\">triangle inequality theorem</a>, we have these three conditions that must all be true if we want a triangle to be possible<BR>\n" );
document.write( "a < b+c<BR>\n" );
document.write( "b < a+c<BR>\n" );
document.write( "c < a+b<BR>\n" );
document.write( "Rephrased verbally: \"The sum of any two sides must exceed the third side\".\r<BR>\n" );
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document.write( "Let's isolate c in the 1st two inequalities<BR>\n" );
document.write( "a < b+c becomes a-b < c<BR>\n" );
document.write( "b < a+c becomes b-a < c\r<BR>\n" );
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document.write( "If b ≥ a, then we'll focus on b-a < c so that the left hand side is nonnegative.\r<BR>\n" );
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document.write( "At the same time, the third inequality condition of the triangle inequality theorem states that c < a+b or c < b+a\r<BR>\n" );
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document.write( "We have these inequalities<BR>\n" );
document.write( "b-a < c and c < b+a<BR>\n" );
document.write( "they can be conveniently glued together to get<BR>\n" );
document.write( "<font color=blue>b-a < c < b+a</font><BR>\n" );
document.write( "This gives a range of possible c values where b ≥ a.\r<BR>\n" );
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document.write( "Summary of the previous section:\r<BR>\n" );
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document.write( "Given a triangle with sides {a,b,c} where a & b are known lengths, and b ≥ a, the third side c has the restrictions of: <font color=blue>b-a < c < b+a</font>\r<BR>\n" );
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document.write( "From here we plug in a = 9 and b = 12<BR>\n" );
document.write( "b-a < c < b+a<BR>\n" );
document.write( "12-9 < c < 12+9<BR>\n" );
document.write( "3 < c < 21\r<BR>\n" );
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document.write( "The third side is between 3 cm and 21 cm, excluding each endpoint. <BR>\n" );
document.write( "We cannot have c = 3. We also cannot have c = 21. <BR>\n" );
document.write( "These endpoints will cause a straight line to form rather than a triangle.\r<BR>\n" );
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document.write( "The following answer choices are in the interval mentioned: <BR>\n" );
document.write( "<font color=red size=4>4 cm<BR>\n" );
document.write( "10 cm<BR>\n" );
document.write( "18 cm</font><BR>\n" );
document.write( "which are the final answers.<BR>\n" );
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