1 month ago

If LM bisects Angle JLK find LJ

Mathematics

1 answer:

Inessa [12.5K]1 month ago

8 0

Answer:

14 units

Step-by-step explanation:

Given: LM bisects $\angle JLK$

To find: LJ

Solution:

By the angle bisector theorem,

an angle bisector of a triangle divides the opposite side into segments that correspond proportionately to the triangle's other two sides.

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

Utilizing the angle bisector theorem,

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

Thus,

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

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