document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=5075>Question 5075</A>: <I><SPAN STYLE=\"word-break: break-all;\"> one side of a triangle is 1 ft longer then the shortest side, and the third side is as long as the shortest side. If the perimeter is less than 25 ft what is the range of the shortest side?\r<BR>\n" );
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document.write( "A= 1/2 ab<BR>\n" );
document.write( "-25= 2a -1/2b = c+ 1\r<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 #2593 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=2593\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> OOPS!!  Rapaljer missed another one!!!\r<BR>\n" );
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document.write( "It was recently brought to my attention by STAN (special thanks to Stan for reminding me about this very important \"detail\" concerning triangles)!  This solution has now been corrected to include this additional restriction, which I have placed at the end of the solution: \r<BR>\n" );
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document.write( "\"In order to be a triangle, the sum of the smaller two sides must be more than the third side.\r<BR>\n" );
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document.write( "Let x = shortest side<BR>\n" );
document.write( "x+1 = second side<BR>\n" );
document.write( "x = third side<BR>\n" );
document.write( "Perimeter = 3x + 1 < 25\r<BR>\n" );
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document.write( "Perimeter must be > 0, so <BR>\n" );
document.write( "0<3x + 1 < 25\r<BR>\n" );
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document.write( "Subtract 1 from each part:  <BR>\n" );
document.write( "0-1< 3x + 1 < 25 - 1<BR>\n" );
document.write( "-1 < 3x < 24\r<BR>\n" );
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document.write( "Divide each part by 3:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F3%3C+3x%2F3+%3C+24%2F3 ALIGN=MIDDLE  ALT=\"-1%2F3%3C+3x%2F3+%3C+24%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F3%3C+x%3C8 ALIGN=MIDDLE  ALT=\"-1%2F3%3C+x%3C8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "However, x represents a side of a triangle, so x must be positive: x>0.  In addition since the sum of the smaller two sides must be greater than the largest side, \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+x+%3E+x%2B1 ALIGN=MIDDLE  ALT=\"+x+%2B+x+%3E+x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract x from each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E+1 ALIGN=MIDDLE  ALT=\"x+%3E+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Final answer:  <BR>\n" );
document.write( "Range of x: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%3Cx%3C8 ALIGN=MIDDLE  ALT=\"+1%3Cx%3C8\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Thanks again, Stan!\r<BR>\n" );
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document.write( "R^2 at SCC </SPAN>\n" );
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