You are given a square piece of land with an area of 1000 square meters. A circular pond is situated within the square land. The radius of the circular pond is 10 meters, and its center is located exactly at the center of the square land. Your task is to remove a rectangular garden inside the square land, parallel to two sides of the square, such that it covers the largest possible area without overlapping with the circular pond.Calculate the dimensions (length and width) of the rectangular garden you need to remove, and determine the remaining area of the square land after the removal.

To solve this problem, we first need to understand the geometry of the situation.

1. The square piece of land has an area of 1000 square meters. To find the side length of the square, we take the square root of the area, which is √1000 = 31.62 meters (rounded to two decimal places).

2. The circular pond has a radius of 10 meters. The diameter of the circle, which is twice the radius, is 20 meters.

3. The rectangular garden must be situated within the square land without overlapping with the circular pond. This means that the width of the rectangle cannot exceed the diameter of the circle, which is 20 meters.

4. The length of the rectangle can be as long as the side length of the square, which is 31.62 meters.

5. Therefore, the dimensions of the rectangular garden are 31.62 meters (length) by 20 meters (width). The area of the rectangle is length times width, which is 31.62 * 20 = 632.4 square meters.

6. To find the remaining area of the square land after the removal of the rectangular garden, we subtract the area of the rectangle from the total area of the square. This gives us 1000 - 632.4 = 367.6 square meters.

So, the dimensions of the rectangular garden are 31.62 meters by 20 meters, and the remaining area of the square land after the removal of the garden is 367.6 square meters.