document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135922>Question 135922</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The hypotenuse of a right angled traingle is 34cm.Find the length of the other two sides if one is 14cm longer than the other. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #99608 by </B><A HREF=/tutors/aboutme.mpl?userid=nycsharkman><B>nycsharkman(136)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nycsharkman><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=99608\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The hypotenuse of a right angled triangle is 34cm. Find the length of the other two sides if one is 14cm longer than the other.\r<BR>\n" );
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document.write( "We use the Pythagorean Theorem:\r<BR>\n" );
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document.write( "a^2 + b^2 = c^2\r<BR>\n" );
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document.write( "Before we do, let's figure out the other parts of the question.\r<BR>\n" );
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document.write( "c^2 = our hypotenuse\r<BR>\n" );
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document.write( "The length of one side is 14 more than the other.\r<BR>\n" );
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document.write( "From this information, I pick up that one side = x and the other side = x + 14\r<BR>\n" );
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document.write( "We now have this:\r<BR>\n" );
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document.write( "Let a^2 = x\r<BR>\n" );
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document.write( "Let b^2 = (x + 14)\r<BR>\n" );
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document.write( "Let c^2 = 34\r<BR>\n" );
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document.write( "We now plug and chug.\r<BR>\n" );
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document.write( "x^2 + (x + 14)^2 = 34^2\r<BR>\n" );
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document.write( "x^2 + x^2 + 28x + 196 = 1156\r<BR>\n" );
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document.write( "2x^2 + 28x + 196 = 1156\r<BR>\n" );
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document.write( "2x^2 + 28x + 196 - 1156 = 0\r<BR>\n" );
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document.write( "2x^2 + 28x - 960 = 0\r<BR>\n" );
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document.write( "Divide every term by 2 to make factoring easier.\r<BR>\n" );
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document.write( "x^2 + 14x - 480 = 0\r<BR>\n" );
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document.write( "We now factor the left side.\r<BR>\n" );
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document.write( "(x + 30) (x - 16) = 0\r<BR>\n" );
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document.write( "Set each factor to 0 and solve for x.\r<BR>\n" );
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document.write( "x + 30 = 0\r<BR>\n" );
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document.write( "x = -30....This answer is REJECTED because length indicates distance and distance CANNOT be negative.  It's like saying the distance from home plate to first base is -90 feet.  Does that make sense?  No!  The distance is 90 feet NOT NEGATIVE 90 feet.\r<BR>\n" );
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document.write( "Back to your question.\r<BR>\n" );
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document.write( "x - 16 = 0\r<BR>\n" );
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document.write( "x = 16cm\r<BR>\n" );
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document.write( "One side of your triangle is 16cm.\r<BR>\n" );
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document.write( "The other side is x + 14cm.\r<BR>\n" );
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document.write( "To find it, replace x with 16cm and add to 14cm.\r<BR>\n" );
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document.write( "Other side of triangle = 16cm + 14cm = 30cm\r<BR>\n" );
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document.write( "Is this clear?\r<BR>\n" );
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document.write( " </SPAN>\n" );
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