Question

NZ is the angle bisector of ∠LNM. What is LZ? Enter the numerical value only.

Answer 1

LZ = 3

Explanation:

given NZ is the angle bisector of ∠ LNM , then it divides the opposite side into segments that are proportional to the other 2 sides, that is

`(LZ)/(MZ)` =
`(NL)/(NM)` ( substitute values )

`(LZ)/(5-LZ)` =
`(3)/(2)` ( cross- multiply )

2 LZ = 3(5 - LZ) ← distribute parenthesis

2 LZ = 15 - 3 LZ ( add 3 LZ to both sides )

5 LZ = 15 ( divide both sides by 5 )

LZ = 3