Respuesta :

Given:

[tex]\begin{gathered} CA=6n \\ EF=n+8 \end{gathered}[/tex]

To find:

The length of EF.

Explanation:

According to the figure,

We can write,

[tex]\frac{BE}{BC}=\frac{EF}{CA}[/tex]

Substituting the given values, we get

[tex]\begin{gathered} \frac{x}{2x}=\frac{n+8}{6n} \\ \frac{1}{2}=\frac{n+8}{6n} \\ 6n=2n+16 \\ 4n=16 \\ n=4 \end{gathered}[/tex]

Therefore, the length of EF will be,

[tex]EF=n+8=4+8=12[/tex]

Final answer:

The length of EF will be 12.

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