document.write( "Question 1177803: The legs of a right triangle are in the ratio 1:2. The
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Algebra.Com's Answer #806962 by Edwin McCravy(20060) $\"\"$ $\"About$

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The legs of a right triangle are in the ratio 1:2.

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document.write( "That means the right triangle is similar to this right triangle\r\n" );
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The angle bisector to the short leg divides it into two
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document.write( "We draw the angle bisector (in green), and let the two segments be \r\n" );
document.write( "x and x+1:\r\n" );
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document.write( "A famous theorem says:\r\n" );
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document.write( "The bisector of an angle of a triangle divides the opposite side into\r\n" );
document.write( "segments that are proportional to the adjacent sides.\r\n" );
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document.write( "We also know the ratio is 2:√5 from the similar right triangle at the top.\r\n" );
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document.write( "Solve for x and get\r\n" );
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document.write( "So the right side of the triangle is  = \r\n" );
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document.write( "Since the side corresponding to 1 is 9+4√5, we know the scale factor is\r\n" );
document.write( "9+4√5.\r\n" );
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document.write( "Since this triangle (the one at the top)\r\n" );
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document.write( "has perimeter 3+√5, we just multiply that by the scale factor:\r\n" );
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document.write( "and get \r\n" );
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document.write( "   <--answer\r\n" );
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document.write( "Edwin

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