Final answer:
The maximum area of a rectangular sandbox with a perimeter of at most 100 feet is achieved when it is a square. By dividing the perimeter by 4, we find a side length of 25 feet, resulting in a maximum area of 625 square feet.
Step-by-step explanation:
The maximum area of a rectangle with a given perimeter is obtained when the rectangle is a square. Since the perimeter of the sandbox that Pedro can build is at most 100 feet, we can find the side length of this square by dividing the perimeter by 4, which represents the four sides of a square. The calculation would be as follows: side length = 100 feet / 4 = 25 feet.
Now to find the maximum area of the sandbox (which is a square in this case), we use the area formula for a square: area = side length × side length. So the area = 25 feet × 25 feet = 625 square feet. Thus, the maximum area of the sandbox is 625 square feet.
A helpful trick when dealing with problems like this is to think about equivalent geometric shapes, like turning the problem of a rectangle with maximum area into the problem of a square with maximum area, given a fixed perimeter. This approach simplifies the process and leads directly to the solution.