document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=101989>Question 101989</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A triangle had the following side lengths:  33 ft, 56 ft and 65 ft. Was it a right triangle? \r<BR>\n" );
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document.write( "Explain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #74149 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=74149\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If this is a right triangle, then the Pythagorean theorem applies. The Pythagorean theorem says<BR>\n" );
document.write( "that in a right triangle the square of the length of the hypotenuse (the longest side) equals<BR>\n" );
document.write( "the sum of the squares of the two remaining sides (called the legs). So if the triangle<BR>\n" );
document.write( "is a right triangle the square of the longest side (65 ft) equals the sum of the square of the<BR>\n" );
document.write( "shortest side (33 ft) plus the square to the remaining side (56 ft). In equation form this <BR>\n" );
document.write( "becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65%5E2+=+33%5E2+%2B+56%5E2 ALIGN=MIDDLE  ALT=\"65%5E2+=+33%5E2+%2B+56%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If this equation is true, then the triangle is a right triangle.<BR>\n" );
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document.write( "On the left side the square of 65 is 65 times 65 which is 4225. On the right side the<BR>\n" );
document.write( "square of 33 is 33 times 33 which is 1089 and the square of 56 is 56 times 56 which is 3136.<BR>\n" );
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document.write( "Substituting these values into the Pythagorean base equation results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4225+=+1089+%2B+3136 ALIGN=MIDDLE  ALT=\"4225+=+1089+%2B+3136\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and adding the two numbers on the right side leads to the equation becoming:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4225+=+4225 ALIGN=MIDDLE  ALT=\"4225+=+4225\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since the Pythagorean equation is true for this triangle, the triangle is a right triangle.<BR>\n" );
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document.write( "Hope this helps you to understand how you can do this problem.<BR>\n" );
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document.write( " </SPAN>\n" );
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