Question

If LM bisects Angle JLK find LJ

Answer 1

Answer:

14 units

Step-by-step explanation:

Given: LM bisects $\angle JLK$

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 $\Delta JKL$, LM bisects $\angle JLK$

Using angle bisector theorem,

$\frac{LK}{LJ}=\frac{KM}{JM}\\\frac{LK}{LJ}=\frac{KM}{JK-MK}\\\frac{8}{x+3}=\frac{4}{x-4}\\8(x-4)=4(x+3)\\8x-32=4x+12\\8x-4x=12+32\\4x=44\\x=\frac{44}{4}=11$

So,

$LJ=x+3=11+3=14\,\,units$