A rectangular plot of land has sides with lengths of 38 m and 52 m correct to the nearest m. Find the range of the possible values of the area of the rectan...

Answer Details

To find the range of possible values for the area of the rectangular plot of land, we need to consider the possible range of lengths of the sides.
Given that the lengths of the sides are 38 m and 52 m, correct to the nearest meter, there is a possibility of some error in the measurements. So, let's consider the minimum and maximum possible lengths for each side.
For the first side with a length of 38 m, the minimum possible length would be 37.5 m (rounded down) and the maximum possible length would be 38.5 m (rounded up).
For the second side with a length of 52 m, the minimum possible length would be 51.5 m (rounded down) and the maximum possible length would be 52.5 m (rounded up).
Now, let's calculate the range of possible areas using these minimum and maximum lengths.
The minimum area of the rectangle would be (37.5 m) * (51.5 m) = 1931.25 m² (rounded to the nearest 0.01 m²).
The maximum area of the rectangle would be (38.5 m) * (52.5 m) = 2021.25 m² (rounded to the nearest 0.01 m²).
Therefore, the range of possible values for the area of the rectangle is 1931.25 m² ≤ A < 2021.25 m².
So, the correct answer is 1931.25 m² ≤ A < 2021.25 m².