document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=255613>Question 255613</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A triangle has sides which are 9, 40, and 41 millimeters long. How could you determine if this triangle is or is not a right triangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187824 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=187824\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We have a thing called the triangle inverse theorem. This has three parts:<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+%3C+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+%3C+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > then triangle is obtuse<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > then triangle is right<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+%3E+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+%3E+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > then triangle is acute<BR>\n" );
document.write( "We also have the triangle inequality statement which says<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+b+%3E+c ALIGN=MIDDLE  ALT=\"a+%2B+b+%3E+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "step 1 - apply our numbers to the inequality and we get<BR>\n" );
document.write( "9+40 > 41. <BR>\n" );
document.write( "So, we have a triangle. Now we put the numbers into the inverse theorem and get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5E2+%2B+%2840%5E2%29+__+41%5E2 ALIGN=MIDDLE  ALT=\"9%5E2+%2B+%2840%5E2%29+__+41%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81+%2B+1600+__+1681 ALIGN=MIDDLE  ALT=\"81+%2B+1600+__+1681\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1681+=+1681 ALIGN=MIDDLE  ALT=\"1681+=+1681\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a right triangle. </SPAN>\n" );
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