Answer:
14 units
Step-by-step explanation:
Given: LM bisects [tex]\angle JLK[/tex]
To find: LJ
Solution:
According to angle bisector theorem,
an angle bisector of a triangle divides the interior angle's opposite side into two segments that are proportional to the other two sides of the triangle.
In [tex]\Delta JKL[/tex], LM bisects [tex]\angle JLK[/tex]
Using angle bisector theorem,
[tex]\frac{LK}{LJ}=\frac{KM}{JM}\\\frac{LK}{LJ}=\frac{KM}{JK-MK}\\\frac{8}{x+3}=\frac{4}{x-4}\\8(x-4)=4(x+3)\\8x-32=4x+12\\8x-4x=12+32\\4x=44\\x=\frac{44}{4}=11[/tex]
So,
[tex]LJ=x+3=11+3=14\,\,units[/tex]
