9514 1404 393
Answer:
LJ = 14
Explanation:
The angle bisector divides corresponding triangle segments proportionally.
LJ/LK = JM/KM
(x+3)/8 = (x-4)/4
x +3 = 2(x -4) . . . . . . multiply by 8
11 = x . . . . . . . . . . . . . add 8-x, simplify
Then the length LJ is ...
LJ = x+3 = 11 +3
LJ = 14