Question

A square plot of land has a building 60 m long and 40 m wide at one corner. The rest ofthe land outside the building forms a parking lot. If the parking lot has an area of 12,000m², what are the dimensions of the entire plot of land?​

Answer 1

The dimensions of the entire square plot of land are 120 meters by 120 meters, calculated by adding the area of the building to the area of the parking lot and then taking the square root to find the side length.

Step-by-step explanation:

To find the dimensions of the entire plot of land when we know the area of the parking lot is 12,000 m² and the dimensions of the building, we can follow these steps:

1. Let's denote the side length of the square plot of land as x meters.
2. Then the total area of the plot would be x².
3. Since the building occupies part of the land, we subtract the area of the building from the total area to get the area of the parking lot: x² - (60 m × 40 m).
4. The area of the building is 60 m × 40 m = 2400 m².
5. Now we can set up the equation: x² - 2400 m² = 12,000 m².
6. Solving for x² gives us x² = 12,000 m² + 2400 m².
7. Therefore, x² = 14,400 m², so x = 120 m.

This means that each side of the square plot of land is 120 meters long. Thus, the dimensions of the whole plot are 120 m × 120 m.