Question

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

Answer 1

$\frac{20}{7}$

Answer 2

Answer:

$LZ=\frac{20}{7}$

Step-by-step explanation:

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

$\frac{MZ}{LZ}=\frac{MN}{NL}$

$\frac{MZ}{LZ}=\frac{3}{4}$                                 (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

$\frac{5-LZ}{LZ}=\frac{3}{4}$

$\frac{5}{LZ}-1=\frac{3}{4}$

$\frac{5}{LZ}=\frac{7}{4}$

$LZ=\frac{20}{7}$