Final answer:
Jada can create a playpen with at least 70 square feet using 35 feet of fencing by constructing a square shape, which would have a maximum enclosed area of 76.56 square feet - big enough for the requirement.
Step-by-step explanation:
Jada wants to create a playpen for her dog with at least 70 square feet of space using 35 feet of fencing. To determine if this is possible, we can calculate the maximum area that can be enclosed with the given amount of fencing.
The most efficient shape for enclosing the maximum area with the minimum perimeter is a circle, but commonly, playpens are in the shape of a square or rectangle.
For simplicity, we will consider a square as it would provide more area than a rectangle with the same perimeter.
For a square:
- Lets assume each side of the square is 's' feet in length.
- The perimeter P of a square is given by P = 4s.
- To find the maximum side length possible with 35 feet of fencing, we set the perimeter to 35 feet, which gives us s = 35 / 4 = 8.75 feet.
- The area A of a square is given by A = s². So, the maximum area Jada can enclose with 35 feet of fencing is 8.75² = 76.56 square feet.
Since 76.56 square feet is greater than 70 square feet, Jada can indeed make a big enough playpen for her dog.