Question

This figure shows △LMN . NZ is the angle bisector of ∠LNM .

What is LZ ?
Enter your answer, as a fraction, in the box.

Answer 1

`LZ=(20)/(7)`

Explanation:

Since, NZ is the angle bisector of ∠LNM , therefore by Angle bisector theorem,

`(MZ)/(LZ)=(MN)/(NL)`

`(MZ)/(LZ)=(3)/(4)` (1)

Also, it is given that ML= 5 and ML=MZ+LZ, then

5=MZ+LZ

MZ=5-LZ

Substituting the value of MZ in equation (1), we get

`(5-LZ)/(LZ)=(3)/(4)`

`(5)/(LZ)-1=(3)/(4)`

`(5)/(LZ)=(7)/(4)`

`LZ=(20)/(7)`

Answer 2

`(20)/(7)`