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

Options

A. (10 `pm` 0.01) m
B. (10 `pm` 0.1) m
C. (10 `pm` 0.02) m
D. (10 `pm` 0.2) m

Answer

To solve the problem of finding the side of a square park given its area, 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: Set up the equation with the given area
We are given that the area \( A \) is \( 100 \pm 0.2 \, m^2 \). This means:
\[ A = 100 \, m^2 \quad \text{and} \quad \Delta A = 0.2 \, m^2 \]

### Step 3: Calculate the side length
Using the area formula:
\[ L^2 = 100 \]
To find \( L \), we take the square root:
\[ L = \sqrt{100} = 10 \, m \]

### Step 4: Calculate the error in the side length
To find the uncertainty in the side length \( \Delta L \), we can use the relationship between the errors in area and side length. The formula relating the error in area to the error in length is:
\[ \frac{\Delta A}{A} = 2 \frac{\Delta L}{L} \]

### Step 5: Substitute the known values into the error formula
Substituting \( \Delta A = 0.2 \, m^2 \) and \( A = 100 \, m^2 \):
\[ \frac{0.2}{100} = 2 \frac{\Delta L}{10} \]

### Step 6: Solve for \( \Delta L \)
Rearranging the equation, we get:
\[ \frac{0.2}{100} = \frac{2 \Delta L}{10} \]
This simplifies to:
\[ \frac{0.2}{100} = \frac{\Delta L}{5} \]
Multiplying both sides by 5:
\[ \Delta L = \frac{0.2 \times 5}{100} = 0.01 \, m \]

### Step 7: Write the final result for the side length with uncertainty
Thus, the side length of the park is:
\[ L = 10 \pm 0.01 \, m \]

### Final Answer
The side of the park is \( 10 \pm 0.01 \, m \).

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