Final answer:
To find the largest area enclosed by the rope, we need to determine the dimensions of the rectangle formed by the rope. The largest area can be obtained when the rectangle is a square with a side length of 15 meters. Therefore, the largest area that can be enclosed by the rope is 225 square meters.
Step-by-step explanation:
To find the largest area that can be enclosed by the rope, we need to determine the dimensions of the rectangle formed by the rope. Since the rope forms a loop of length 30 meters, the perimeter of the rectangle is twice the length of the loop, which is 60 meters.
A rectangle has a maximum area when it is a square. So, we need to find the side length of the square that has a perimeter of 60 meters. The formula for the perimeter of a square is 4s, where s is the side length. Setting 4s equal to 60 and solving for s, we get s = 15 meters.
Therefore, the largest area that can be enclosed by the rope is obtained when the rectangle is a square with side length 15 meters. The area of a square is given by the formula A = s^2, where s is the side length. Plugging in s = 15, we find that the largest area is 225 square meters.