document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=255064>Question 255064</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sides of an equilateral triangle are shortened by 12 units,13 units and 14 units respectively and a right angled triangle is formed.Find the side of the equilateral triangle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187365 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=187365\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = 17.\r<BR>\n" );
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document.write( "17 - 14 = 3<BR>\n" );
document.write( "17 - 13 = 4<BR>\n" );
document.write( "17 - 12 = 5\r<BR>\n" );
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document.write( "345 triangle is a right triangle.\r<BR>\n" );
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document.write( "solve by use of pythatogrean formula.\r<BR>\n" );
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document.write( "a^2 + b^2 = c^2\r<BR>\n" );
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document.write( "x is the side of the equilateral triangle.\r<BR>\n" );
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document.write( "(x-12) = largest side which would be equal to c.\r<BR>\n" );
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document.write( "(x-13) = midsize side which would be equal to b.\r<BR>\n" );
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document.write( "(x-14) = smallest side which would be equal to a.\r<BR>\n" );
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document.write( "a^2 + b^2 = c^2 becomes:\r<BR>\n" );
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document.write( "(x-14)^2 + (x-13)^2 = (x-12)^2\r<BR>\n" );
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document.write( "this becomes\r<BR>\n" );
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document.write( "x^2 - 28x + 196 + x^2 - 26x + 169 = x^2 - 24x + 144\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "2x^2 - 54x + 365 = x^2 - 24x + 144\r<BR>\n" );
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document.write( "subtract x^2 from both sides of equation to get:\r<BR>\n" );
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document.write( "x^2 - 54x + 365 = -24x + 144\r<BR>\n" );
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document.write( "add 24x to both sides of equation to get:\r<BR>\n" );
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document.write( "x^2 - 30x + 365  = 144\r<BR>\n" );
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document.write( "subtract 144 from both sides of equation to get:\r<BR>\n" );
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document.write( "x^2 - 30x + 221 = 0\r<BR>\n" );
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document.write( "factor this quadratic equation to get:\r<BR>\n" );
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document.write( "(x-17) * (x-13) = 0\r<BR>\n" );
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document.write( "this makes x = 17 or x = 13.\r<BR>\n" );
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document.write( "x can't be 13 because then one of the sides of the triangle will be 0.\r<BR>\n" );
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document.write( "x has to be 17.\r<BR>\n" );
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document.write( "when x is 17, you get:\r<BR>\n" );
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document.write( "x-12 = 17-12 = 5<BR>\n" );
document.write( "x-13 = 17-13 = 4<BR>\n" );
document.write( "x-14 = 17-14 = 3\r<BR>\n" );
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document.write( "that's your 345 triangle which is a right triangle.\r<BR>\n" );
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document.write( "side of the equilateral triangle is 17.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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