document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=297609>Question 297609</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the Pythagorean theorem to find the length of the unknown side of the triangle.<BR>\n" );
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document.write( "Square root of 17 is one side.<BR>\n" );
document.write( "Square root of 5 is the second side.<BR>\n" );
document.write( "And x is the third side. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #214277 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=214277\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Pythagorean Theorem is c^2 = a^2 + b^2\r<BR>\n" );
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document.write( "c is the hypotenuse and a and b are the legs of the right triangle.\r<BR>\n" );
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document.write( "The hypotenuse is always bigger than either of the 2 legs.\r<BR>\n" );
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document.write( "You are given that one side of the triangle is equal to sqrt(17).\r<BR>\n" );
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document.write( "You are also given that the second side of the triangle is equal to sqrt(5).\r<BR>\n" );
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document.write( "sqrt(5) cannot be the hypotenuse of the right triangle.\r<BR>\n" );
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document.write( "sqrt(17) could.\r<BR>\n" );
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document.write( "sqrt(x) could also, since you do not know what size that is.\r<BR>\n" );
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document.write( "Assuming that x is the hypotenuse of the triangle, then the Pythagorean formula would be:\r<BR>\n" );
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document.write( "x^2 = 17 + 5\r<BR>\n" );
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document.write( "c^2 = x^2<BR>\n" );
document.write( "a^2 = 17<BR>\n" );
document.write( "b^2 = 5\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( "x^2 = 23\r<BR>\n" );
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document.write( "That would make x = sqrt(23).\r<BR>\n" );
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document.write( "Assuming that 17 is the hypotenuse of the triangle, then the Pythagorean formula would be:\r<BR>\n" );
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document.write( "17 = 5 + x^2\r<BR>\n" );
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document.write( "c^2 = 17<BR>\n" );
document.write( "a^2 = 5<BR>\n" );
document.write( "b^2 = x^2\r<BR>\n" );
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document.write( "Subtract 5 from both sides of that equation to get:\r<BR>\n" );
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document.write( "x^2 = 17 - 5\r<BR>\n" );
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document.write( "Combine like terms to get:\r<BR>\n" );
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document.write( "x^2 = 12\r<BR>\n" );
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document.write( "That would make x = sqrt(12).\r<BR>\n" );
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document.write( "Either answer would be correct if it was not specified which side was which.\r<BR>\n" );
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document.write( "In a right triangle, the Pythagorean Formula holds:\r<BR>\n" );
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document.write( "c^2 = a^2 + b^2\r<BR>\n" );
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document.write( "With our first triangle, this becomes:\r<BR>\n" );
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document.write( "5 + 17 = 23\r<BR>\n" );
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document.write( "With our second triangle, this becomes:\r<BR>\n" );
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document.write( "5 + 12 = 17\r<BR>\n" );
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document.write( "One of these will be your correct answer once you determine which side was supposed to be 5 and which side was supposed to be 17.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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