document.write( "Question 1106163: vt is an angle bisector of angle svu. If sv=9,vu=20,su=27, find st
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Algebra.Com's Answer #721102 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "In any triangle, the angle bisector divides the side to which it is drawn, in two segments proportional to the ratio \r\n" );
document.write( "of two other sides of a triangle.\r\n" );
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document.write( "    For this theorem and its proof, see the lesson\r\n" );
document.write( "        On what segments the angle bisector divides the side of a triangle\r\n" );
document.write( "    in this site.\r\n" );
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document.write( "Using this theorem for the triangle SVU, you get the proportion\r\n" );
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document.write( " = ,   or    = .\r\n" );
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document.write( "The second equation is  |ST| + |TU| = 27.\r\n" );
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document.write( "Introducing for breavity x = |ST|, y = |TU|,  you have this system of 2 equations\r\n" );
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document.write( "20x - 9y = 0,       (1)\r\n" );
document.write( "  x +  y = 27.      (2)\r\n" );
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document.write( "To solve it, use the Elimination method. For it, multiply eq(2) by 9 (both sides). Keep eq(1) as is. You will get\r\n" );
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document.write( "20x -  9y =   0,    (1)\r\n" );
document.write( " 9x +  9y = 243.    (2)\r\n" );
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document.write( "Next add equations (1) and (2). You will get\r\n" );
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document.write( "29x = 243.\r\n" );
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document.write( "Hence,  x = |ST| = .\r\n" );
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