document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=923629>Question 923629</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If there is a triangle which has sides of 60, 80 and 100 for lengths and you split the triangle so that it creates 2 right triangles (separating the triangle on the 100 length side) what would be the lengths of the 4 new sides which have been created? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #560190 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=560190\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you will have 2 triangles.<BR>\n" );
document.write( "the first triangle will have sides of 36, 48, 60<BR>\n" );
document.write( "the second triangle will have sides of 64, 48, 80\r<BR>\n" );
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document.write( "you drop a perpendicular from the vertex of the angle opposite the 100 length side and perpendicular to it.\r<BR>\n" );
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document.write( "your 100 length is split into 2 pieces.<BR>\n" );
document.write( "one piece is x units in length.<BR>\n" );
document.write( "the other piece is 100 - x units in length.\r<BR>\n" );
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document.write( "your altitude has a length of z units.\r<BR>\n" );
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document.write( "since you have 2 right triangles with a common altitude, you can set up an equation using the pythagorean formula as follows:\r<BR>\n" );
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document.write( "x^2 + z^2 = 60^2 for the first triangle.\r<BR>\n" );
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document.write( "(100-x)^2 + z^2 = 80^2 for the second triangle.\r<BR>\n" );
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document.write( "solve both of these equations for z^2 and you get:\r<BR>\n" );
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document.write( "z^2 = 60^2 - x^2 and z^2 = 80^2 - (100 - x)^2\r<BR>\n" );
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document.write( "since both expressions on the right sides of these equations are equal to z^2, you can set them equal to each other to get:\r<BR>\n" );
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document.write( "60^2 - x^2 = 80^2 - (100 - x)^2\r<BR>\n" );
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document.write( "solve this equation for x and you get x = 36.\r<BR>\n" );
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document.write( "that makes 100 - x = 64.\r<BR>\n" );
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document.write( "you can use either equation to solve for z and you will get z = 48.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "z^2 = 60^2 - x^2 becomes z^2 = 60^2 - 36^2 which makes z^2 = 2304 which makes z = 48.\r<BR>\n" );
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document.write( "solve for z^2 in the other equation and you will get the same answer.\r<BR>\n" );
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document.write( "z will be equal to 48 in that other equation as well.\r<BR>\n" );
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document.write( "confirm your solutions by using the pythagorean formula on each triangle and you will see that the values given for x and 100-x and z are good in both triangles.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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