document.write( "Question 1117342: *I don't know how to add pictures on here, if anyone could help that'd be great!*\r
\n" ); document.write( "\n" ); document.write( "So I have a triangle (△PQR) and it's perimeter is 40.
\n" ); document.write( "In △PQR, there is an angle bisector (PL).
\n" ); document.write( "Given: Perimeter of △PQR = 40; LR = 15; LQ = 9\r
\n" ); document.write( "\n" ); document.write( "FIND PQ\r
\n" ); document.write( "\n" ); document.write( "The answer is 6. \r
\n" ); document.write( "\n" ); document.write( "My problem is I don't know how to get the answer 6. I do know you have to do a proportion but from all the numbers I've tried, haven't been able to get 6. \n" ); document.write( "

Algebra.Com's Answer #732390 by ikleyn(52873) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Use the theorem:\r\n" );
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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 of two other sides of a triangle\r\n" );
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document.write( "    (See the lesson On what segments the angle bisector divides the side of a triangle  in this site).\r\n" );
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document.write( "So, |PR| = 15x,  |PQ| = 9x,  where x is an unknown common measure of the segments PR  and  PQ.\r\n" );
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document.write( "Thus for the perimeter you have\r\n" );
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document.write( "15x + 9x + (15+9) = 40  ====>\r\n" );
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document.write( "24x = 40 - (15+9) = 16  ====>  x =  = .\r\n" );
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document.write( "Then  |RL| = 15x =  = 10   and  |PQ| = 9x =  = 6.\r\n" );
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document.write( "Answer.  |PQ| = 6.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "The key to the solution is the theorem referred above.\r
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