Answer:
The perimeter of △EFG is [tex]62\ units[/tex]
Step-by-step explanation:
we know that
In the figure the smaller triangle and triangle EFG are similar by AA Similarity Theorem
so
Remember that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
Find the length side EG
[tex]\frac{9}{EF}=\frac{14}{EG}[/tex]
substitute the given values
[tex]\frac{9}{9+9}=\frac{14}{EG}[/tex]
[tex]\frac{9}{18}=\frac{14}{EG}[/tex]
[tex]\frac{1}{2}=\frac{14}{EG}[/tex]
[tex]EG=14(2)=28\ units[/tex]
Find the perimeter of △EFG
[tex]P=EF+EG+FG[/tex]
substitute
[tex]P=2(9)+28+2(8)[/tex]
[tex]P=62\ units[/tex]
