A path of uniform width surrounds a circular park. The difference of internal and external circumferences of this circular path is 132 metres. Its width is :
(Take `pi= (22)/(7)`)

Options

A. 22 m
B. 20 m
C. 21 m
D. 24 m

Answer

To solve the problem, we need to find the width of the path surrounding a circular park given the difference between the internal and external circumferences is 132 meters.

### Step-by-Step Solution:

1. **Understand the Circumference Formula**:
The circumference \( C \) of a circle is given by the formula:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle.

2. **Identify the Radii**:
Let:
- \( r \) = radius of the circular park (internal radius)
- \( R \) = radius of the circular park plus the width of the path (external radius)

3. **Write the Circumference Equations**:
- The internal circumference (C1) is:
\[ C_1 = 2 \pi r \]
- The external circumference (C2) is:
\[ C_2 = 2 \pi R \]

4. **Set Up the Equation for the Difference**:
According to the problem, the difference between the external and internal circumferences is 132 meters:
\[ C_2 - C_1 = 132 \]
Substituting the expressions for \( C_1 \) and \( C_2 \):
\[ 2 \pi R - 2 \pi r = 132 \]

5. **Factor Out Common Terms**:
Factor out \( 2 \pi \) from the left side:
\[ 2 \pi (R - r) = 132 \]

6. **Solve for the Width**:
The width of the path is given by \( R - r \). Thus, we can express it as:
\[ R - r = \frac{132}{2 \pi} \]

7. **Substitute the Value of \( \pi \)**:
Given \( \pi = \frac{22}{7} \), we substitute this value into the equation:
\[ R - r = \frac{132}{2 \times \frac{22}{7}} = \frac{132 \times 7}{44} \]

8. **Simplify the Calculation**:
Simplifying the fraction:
\[ R - r = \frac{132 \times 7}{44} = \frac{924}{44} = 21 \]

9. **Conclusion**:
Therefore, the width of the path surrounding the circular park is:
\[ \text{Width} = 21 \text{ meters} \]