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

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

This figure shows LMN NZ is the angle bisector of LNM What is LZ Enter your answer as a fraction in the box class=

Respuesta :

[tex] \frac{20}{7} [/tex]
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Answer:

[tex]LZ=\frac{20}{7}[/tex]

Step-by-step explanation:

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

[tex]\frac{MZ}{LZ}=\frac{MN}{NL}[/tex]

[tex]\frac{MZ}{LZ}=\frac{3}{4}[/tex]                                 (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

[tex]\frac{5-LZ}{LZ}=\frac{3}{4}[/tex]

[tex]\frac{5}{LZ}-1=\frac{3}{4}[/tex]

[tex]\frac{5}{LZ}=\frac{7}{4}[/tex]

[tex]LZ=\frac{20}{7}[/tex]

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