document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=896676>Question 896676</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the hypotenuse of a right angled triangle is 20cm. the difference between its other two sides be 4cm. The sides are </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #543701 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=543701\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> hypotenuse is 20.\r<BR>\n" );
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document.write( "one of the sides is x.<BR>\n" );
document.write( "the other side is (x+4)\r<BR>\n" );
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document.write( "pythagorus says:\r<BR>\n" );
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document.write( "x^2 + (x+4)^2 = 20^2 which becomes:\r<BR>\n" );
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document.write( "x^2 + x^2 + 8x + 16 = 400\r<BR>\n" );
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document.write( "subtract 400 from both sides of the equation and combine like terms to get:\r<BR>\n" );
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document.write( "2x^2 + 8x - 384 = 0\r<BR>\n" );
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document.write( "divide both sides of the equation by 2 to get:\r<BR>\n" );
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document.write( "x^2 + 4x - 192 = 0\r<BR>\n" );
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document.write( "factor to get:\r<BR>\n" );
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document.write( "(x + 16) * (x - 12) = 0\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = -16 or x = 12\r<BR>\n" );
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document.write( "x can't be negative so the solution is x = 12\r<BR>\n" );
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document.write( "if x = 12, then x+4 = 16\r<BR>\n" );
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document.write( "your sides are 12 and 16.\r<BR>\n" );
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document.write( "by pythagorus, 12^2 + 16^2 = 20^2 which becomes:\r<BR>\n" );
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document.write( "144 + 256 = 400 which becomes:\r<BR>\n" );
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document.write( "400 = 400 confirming the solution is good.\r<BR>\n" );
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document.write( "the sides are 12 and 16 and the hypotenuse is 20\r<BR>\n" );
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document.write( "this triangle is similar to a 3/4/5 triangle since 12/16/20 is a multiple of 3/4/5 by a factor of 4.\r<BR>\n" );
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document.write( "the triangles have the same angles and the sides are proportional which is the definition of similar triangles.\r<BR>\n" );
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document.write( "you didn't need to know that.\r<BR>\n" );
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document.write( "it's an extra.\r<BR>\n" );
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document.write( "your solution is that the sides are 12 and 16.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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