Posted by Mona on .
Find KN and LM. In triangle LKM, angle L is bisected. Line segment LK is 11, line segment KN is x4, line segment NM is 5.4, and line segment LM is 2x + 1.3
(there is a drawing of this triangle)
Thanks.

Geometry8th gr 
Reiny,
I assume the bisector of angle L is LN where N is on KM
In the Post
http://www.jiskha.com/display.cgi?id=1359738761
I proved for you , and Steve called it, the angle bisector theorem
In this case:
KL/KN = LM/MN
11/(x4) = (2x+1.3)/5.4
2x^2  6.7x  5.2 = 59.4
2x^2  6.7x  64.6 = 0
20x^2  67x  646 = 0
x = (67 ± √56169)/40
= 7.6 or a negative which will not work in 2x+1.3
KN = x4 = 7.6  4 = 3.6
LM = 2x+1.3 = 15.2 + 1.3 = 16.5
check:
LK/KN = 11/3.6 = 55/18
LM/MN = 16.5/5.4 = 55/18 
Geometry8th gr 
Mona,
Thanks.