document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=557587>Question 557587</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a square has side length 9 in, what is the lenght of the longest line segment that can be drawn between any two points of the square? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #362670 by </B><A HREF=/tutors/aboutme.mpl?userid=neatmath><B>neatmath(302)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=neatmath><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=neatmath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=362670\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><font face=\"Tahoma\">The longest line segment that can be drawn from any 2 points on a square,<br>\r<BR>\n" );
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document.write( "must naturally be a diagonal of a square.  No other possible line segment will be as long as any diagonal of the square.<br>\r<BR>\n" );
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document.write( "You can test this out with any ruler, and any true square.<br>\r<BR>\n" );
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document.write( "So, given a side of 9 cm, we can use the Pythagorean Theorem to find the length of the diagonal of the square.<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5E2%2B9%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"9%5E2%2B9%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81%2B81=c%5E2 ALIGN=MIDDLE  ALT=\"81%2B81=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=162=c%5E2 ALIGN=MIDDLE  ALT=\"162=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28162%29=c ALIGN=MIDDLE  ALT=\"sqrt%28162%29=c\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%28162%29=c ALIGN=MIDDLE  ALT=\"-sqrt%28162%29=c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "Since we are dealing with distances, we can discard the negative solution.<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%28162%29 ALIGN=MIDDLE  ALT=\"c=sqrt%28162%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%2881%2A2%29 ALIGN=MIDDLE  ALT=\"c=sqrt%2881%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=9%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"c=9%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  which is the exact answer<br>\r<BR>\n" );
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document.write( "The longest line segment would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"9%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm.<br>\r<BR>\n" );
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document.write( "Alternatively, we can find an approximation for this answer:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=12.73 ALIGN=MIDDLE  ALT=\"c=12.73\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm<br>\r<BR>\n" );
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document.write( "Using the familiar rules of geometry, and recognizing that a square is cut into two 45-45-90 triangles by a diagonal,<br>\r<BR>\n" );
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document.write( "we could have immediately determined the length of the diagonal to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"9%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm long.<br>\r<BR>\n" );
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document.write( "But then we wouldn't have had the nice opportunity to use the Pythagorean Theorem!<br>\r<BR>\n" );
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document.write( "I hope this helps!  :)<br>\r<BR>\n" );
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document.write( "Email Scott King: neatmath@yahoo.com for help with specific problems,<br>\r<BR>\n" );
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