Final answer:
The ratio of the perimeters of the two similar pentagons is approximately 2:3.
Step-by-step explanation:
To find the ratio of the perimeters, we need to understand the relationship between the areas and the perimeters of similar figures. In this case, the ratio of the areas of the two pentagons is given as 50 ft² : 98 ft². Since the areas are proportional to the square of the lengths, we can find the ratio of the lengths of the sides by taking the square root of the ratio of the areas. The square root of 50/98 is approximately 0.71. Therefore, the ratio of the perimeters of the two pentagons is approximately 0.71:1 or approximately 2:3.