document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1146157>Question 1146157</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A triangle has sides with lengths of 15 yards, 17 yards, and 19 yards. Is it a right triangle?<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 #767459 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=767459\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "A triangle is a right triangle if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"c%5E2+=+a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Given that requirement, if the side lengths are integers, then c has to be odd and exactly one of a and b has to be odd.<br><BR>\n" );
document.write( "Since the given side lengths are all odd, you can tell it is not a right triangle without doing any calculations.<br><BR>\n" );
document.write( "Depending on your level of knowledge, you might not understand that explanation.  So let's make it a little easier.<br><BR>\n" );
document.write( "a and b are both odd, so a^2 and b^2 are both odd; then c^2 = a^2+b^2 is odd plus odd equals even.  But c is odd so c^2 is odd.<br><BR>\n" );
document.write( "So the side lengths can't all be odd integers. </SPAN>\n" );
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