Question

If LM bisects Angle JLK find LJ

Answer 1

14 units

Explanation:

Answer 2

14 units

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,

`(LK)/(LJ)=(KM)/(JM)\\(LK)/(LJ)=(KM)/(JK-MK)\\(8)/(x+3)=(4)/(x-4)\\8(x-4)=4(x+3)\\8x-32=4x+12\\8x-4x=12+32\\4x=44\\x=(44)/(4)=11`

So,

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