Answer:
C. 102 meters.
Step-by-step explanation:
Since we know that dilation changes the all sides of any figure with the same factor.
We have been given two parallelograms and lengths of their corresponding sides. We can see that side length 3.5 m corresponds to side length 21 m. Let us find factor of dilation from our given side lengths.
[tex]\text{Factor of dilation}=\frac{21}{3.5}[/tex]
[tex]\text{Factor of dilation}=6[/tex]
The factor of dilation is 6, which means that sides of larger parallelogram are 6 times the sides of smaller parallelogram.
We have been given that perimeter of smaller parallelogram is 17 meters, therefore, the perimeter of our larger parallelogram will be 6 times the perimeter of smaller parallelogram.
[tex]\text{Perimeter of larger parallelogram}=6\times 17[/tex]
[tex]\text{Perimeter of larger parallelogram}=102[/tex]
Therefore, the perimeter of larger parallelogram will be 102 meters and option C is the correct choice.
