SOLUTION: *I don't know how to add pictures on here, if anyone could help that'd be great!* So I have a triangle (△PQR) and it's perimeter is 40. In △PQR, there is an angle

Algebra ->  Triangles -> SOLUTION: *I don't know how to add pictures on here, if anyone could help that'd be great!* So I have a triangle (△PQR) and it's perimeter is 40. In △PQR, there is an angle       Log On


   

Question 1117342: *I don't know how to add pictures on here, if anyone could help that'd be great!*
So I have a triangle (△PQR) and it's perimeter is 40.
In △PQR, there is an angle bisector (PL).
Given: Perimeter of △PQR = 40; LR = 15; LQ = 9
FIND PQ
The answer is 6.
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.
Answer by ikleyn(52851) About Me  (Show Source):
You can put this solution on YOUR website!
.
Use the theorem:


    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


    (See the lesson On what segments the angle bisector divides the side of a triangle  in this site).



So, |PR| = 15x,  |PQ| = 9x,  where x is an unknown common measure of the segments PR  and  PQ.


Thus for the perimeter you have

15x + 9x + (15+9) = 40  ====>

24x = 40 - (15+9) = 16  ====>  x = 16%2F24 = 2%2F3.


Then  |RL| = 15x = 15%2A%282%2F3%29 = 10   and  |PQ| = 9x = 9%2A%282%2F3%29 = 6.


Answer.  |PQ| = 6.

Solved.

The key to the solution is the theorem referred above.