document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1089361>Question 1089361</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the range of possible measures of x if each set of expressions represents measures of the sides of a triangle.<BR>\n" );
document.write( "x+2,x+4,x+6<BR>\n" );
document.write( "Thank you very much. God bless you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #703748 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=703748\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Obviously, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2%3Cx%2B4%3Cx%2B6 ALIGN=MIDDLE  ALT=\"x%2B2%3Cx%2B4%3Cx%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > , because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%3C4%3C6 ALIGN=MIDDLE  ALT=\"2%3C4%3C6\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2 ALIGN=MIDDLE  ALT=\"x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4 ALIGN=MIDDLE  ALT=\"x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B6 ALIGN=MIDDLE  ALT=\"x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "are the lengths of the side of a triangle,<BR>\n" );
document.write( "they should all be positive values,<BR>\n" );
document.write( "and for that it is enough to require that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2%3E0 ALIGN=MIDDLE  ALT=\"x%2B2%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E-2 ALIGN=MIDDLE  ALT=\"x%3E-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "You know that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B6 ALIGN=MIDDLE  ALT=\"x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the length of the longest side.<BR>\n" );
document.write( "You would also know that the length of the longest side<BR>\n" );
document.write( "must be less than the sum of the lengths of the other two sides.<BR>\n" );
document.write( "That means<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%2B%28x%2B4%29%3Ex%2B6 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%2B%28x%2B4%29%3Ex%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B6%3Ex%2B6 ALIGN=MIDDLE  ALT=\"2x%2B6%3Ex%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and subtracting x and 6 from both sides,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%3E0%29 ALIGN=MIDDLE  ALT=\"highlight%28x%3E0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That shows you the range of possible measures for x.<BR>\n" );
document.write( "In interval notation, it would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%28+0+%2C%22 ALIGN=MIDDLE  ALT=\"%22%28+0+%2C%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%29%22 ALIGN=MIDDLE  ALT=\"%22%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is all that is required for x.<BR>\n" );
document.write( " <BR>\n" );
document.write( "EXPLANATIONS AND MORE:<BR>\n" );
document.write( "As long as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E0 ALIGN=MIDDLE  ALT=\"x%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you could draw such a triangle.<BR>\n" );
document.write( "With <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E-2 ALIGN=MIDDLE  ALT=\"x%3E-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , all three expressions given have positive values,<BR>\n" );
document.write( "and knowing their values you could easily build a triangle with two sides measuring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2 ALIGN=MIDDLE  ALT=\"x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4 ALIGN=MIDDLE  ALT=\"x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "You could just start by drawing those sides as segments AB and AC,<BR>\n" );
document.write( "connected at A, forming any angle BAC, like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing+%28300%2C200%2C-2%2C28%2C-1.5%2C18.5%2C%0D%0Aline%280%2C0%2C27%2C0%29%2Cline%280%2C0%2C10%2C17.32%29%2C%0D%0Alocate%28-0.5%2C0%2CA%29%2Clocate%2827%2C0%2CC%29%2C%0D%0Alocate%2810.2%2C18.5%2CB%29%2Cred%28arc%280%2C0%2C7%2C7%2C-60%2C0%29%29%2C%0D%0Alocate%283%2C3%2Cred%28BAC%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then, all you would have to do is draw a third side, by connecting points B and C with a straight line.<BR>\n" );
document.write( "The distance along that straight segment BC would have be shorter than the sum of the length of the other two sides,<BR>\n" );
document.write( "but making angle BAC smaller or larger,<BR>\n" );
document.write( "you could give the third side any positive length smaller than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%2B%28x%2B4%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%2B%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "A straight line is the shorter distance between two points, such as B and C.<BR>\n" );
document.write( "Common sense tells you that.<BR>\n" );
document.write( "A geometry teacher tells you that the length of a side of a triangle is less that the sum of the lengths of the other two sides.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Drawing a triangle, with specified measures for only two of the sides is easy.<BR>\n" );
document.write( "If the lengths of all three sides are specified,<BR>\n" );
document.write( "it may be possible to draw/construct a triangle to meet the reasonable specifications,<BR>\n" );
document.write( "but it may require either knowledge of geometry constructions,<BR>\n" );
document.write( "or the common sense a carpenter or gardener would have.<BR>\n" );
document.write( "How would you do it in geometry class?<BR>\n" );
document.write( "How would you do it as a gardener? </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );