A public park , in the form of a square , has an area of `(100pm0.2 ) m^2` The side of park is

Options

A. `(10pm0.01)m`
B. `(10pm0.1)m`
C. `(10.0pm0.1)m`
D. `(10.0pm0.2)m`

Answer

To find the side length of a square park given its area and the associated error, we can follow these steps:

### Step 1: Understand the relationship between area and side length
The area \( A \) of a square is given by the formula:
\[ A = L^2 \]
where \( L \) is the length of one side of the square.

### Step 2: Given values
The area of the park is given as:
\[ A = 100 \pm 0.2 \, m^2 \]

### Step 3: Calculate the side length without error
To find the side length \( L \) without considering the error, we take the square root of the area:
\[ L = \sqrt{A} = \sqrt{100} = 10 \, m \]

### Step 4: Calculate the relative error in area
The relative error in the area can be calculated using the formula:
\[ \frac{\Delta A}{A} = 2 \frac{\Delta L}{L} \]
where \( \Delta A \) is the error in area and \( \Delta L \) is the error in length.

### Step 5: Substitute the known values
Substituting the values into the equation:
\[ \Delta A = 0.2 \, m^2, \quad A = 100 \, m^2 \]
we have:
\[ \frac{0.2}{100} = 2 \frac{\Delta L}{10} \]

### Step 6: Simplify the equation
This simplifies to:
\[ 0.002 = 2 \frac{\Delta L}{10} \]
\[ 0.002 = \frac{2 \Delta L}{10} \]
\[ 0.002 = 0.2 \Delta L \]

### Step 7: Solve for \( \Delta L \)
Now, solving for \( \Delta L \):
\[ \Delta L = \frac{0.002}{0.2} = 0.01 \, m \]

### Step 8: Final result
The side length \( L \) with its error is:
\[ L = 10 \pm 0.01 \, m \]

### Conclusion
Thus, the side of the park is:
\[ 10 \, m \pm 0.01 \, m \]

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