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
\(\frac{5-LZ}{LZ}=\frac{3}{4}\)
\(\frac{5}{LZ}-1=\frac{3}{4}\)
\(\frac{5}{LZ}=\frac{7}{4}\)
\(LZ=\frac{20}{7}\)
