A circular wire of length 264 cm is cut and bent in the form of a rectangle whose sides are in the ratio 6 : 5. The smaller side of the rectangler is

Options

A. 30 cm
B. 60 cm
C. 72 cm
D. 132 cm

Answer

To solve the problem, we need to find the smaller side of a rectangle formed by bending a circular wire of length 264 cm, where the sides of the rectangle are in the ratio 6:5.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have a circular wire of length 264 cm.
- This wire is bent to form a rectangle with sides in the ratio of 6:5.

2. **Defining the Sides of the Rectangle**:
- Let the length of the rectangle be \( L = 6x \).
- Let the breadth of the rectangle be \( B = 5x \).
- Here, \( x \) is a common multiplier.

3. **Calculating the Perimeter of the Rectangle**:
- The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2(L + B) \]
- Substituting the values of \( L \) and \( B \):
\[ P = 2(6x + 5x) = 2(11x) = 22x \]

4. **Setting Up the Equation**:
- Since the perimeter of the rectangle is equal to the length of the wire, we can set up the equation:
\[ 22x = 264 \]

5. **Solving for \( x \)**:
- To find \( x \), divide both sides of the equation by 22:
\[ x = \frac{264}{22} \]
- Simplifying the right side:
\[ x = 12 \]

6. **Finding the Length and Breadth**:
- Now that we have \( x \), we can find the dimensions of the rectangle:
- Length \( L = 6x = 6 \times 12 = 72 \) cm
- Breadth \( B = 5x = 5 \times 12 = 60 \) cm

7. **Identifying the Smaller Side**:
- The smaller side of the rectangle is the breadth, which is \( 60 \) cm.

### Conclusion:
The smaller side of the rectangle is **60 cm**.