\r\n" );
document.write( "Here is a triangle drawn to scale with AC = 25, and BD = 20. \r\n" );
document.write( "But as you see, it cannot have a right angle at B. The\r\n" );
document.write( "altitude BD = 20 is just too long to have a right angle at B.\r\n" );
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document.write( "
\r\n" );
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document.write( "Here is a triangle also drawn with he same AC = 25 as the\r\n" );
document.write( "first that has a right angle at B. However the altitude\r\n" );
document.write( "is only about 12.2, not 20.\r\n" );
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document.write( "
\r\n" );
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document.write( "This makes us believe that it is impossible to have such a\r\n" );
document.write( "triangle.\r\n" );
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document.write( "To show that it is impossible, let's suppose that the altitude\r\n" );
document.write( "BD is actually 20 and angle B is a right angle. Let DC = x, then\r\n" );
document.write( "AD will = 25-x.\r\n" );
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document.write( "\r\n" );
document.write( "
\r\n" );
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document.write( "Then triangle ADB is similar to triangle BDC, so\r\n" );
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document.write( "
\r\n" );
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document.write( "
\r\n" );
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document.write( "Cross-multiplying:\r\n" );
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document.write( "
\r\n" );
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document.write( "
\r\n" );
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document.write( "
\r\n" );
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document.write( "However this quadratic has no real solutions,\r\n" );
document.write( "because its discriminant is negative:\r\n" );
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document.write( "
\r\n" );
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document.write( "Therefore we have proved that there is no such triangle.\r\n" );
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document.write( "Edwin
\n" );
document.write( "![\"\"](\"/images/stars/stars-13.gif\")
