Given:
EJ = 5
JH = 20
FG = 8.
If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.
Therefore, we have,
[tex]\frac{EJ}{JH}=\frac{EF}{FG}[/tex]Substituitng the values, EF can be calculated as,
[tex]\begin{gathered} \frac{5}{20}=\frac{EF}{8} \\ 8\times5=20\times EF \\ EF=\frac{40}{20}=2 \end{gathered}[/tex]Therefore, EG can be calculated as,
[tex]EG=EF+FG=2+8=10[/tex]