The circumference of a circle is equal to the perimeter of a rectangle. The length and the breadth of the rectangle are 45 cm and 43 cm, respectively. What is the half the radius of the circle?

Options

A. 56 cm
B. 14 cm
C. 28 cm
D. 7 cm

Answer

To solve the problem, we need to find half the radius of a circle whose circumference is equal to the perimeter of a rectangle with given dimensions. Here’s a step-by-step solution:

### Step 1: Find the perimeter of the rectangle.
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2 \times (\text{length} + \text{breadth}) \]
Given:
- Length \( l = 45 \, \text{cm} \)
- Breadth \( b = 43 \, \text{cm} \)

Substituting the values:
\[ P = 2 \times (45 + 43) = 2 \times 88 = 176 \, \text{cm} \]

### Step 2: Set the circumference of the circle equal to the perimeter of the rectangle.
The formula for the circumference \( C \) of a circle is:
\[ C = 2\pi r \]
Since the circumference is equal to the perimeter of the rectangle, we have:
\[ 2\pi r = 176 \]

### Step 3: Solve for the radius \( r \).
To find \( r \), we rearrange the equation:
\[ r = \frac{176}{2\pi} = \frac{88}{\pi} \]

### Step 4: Calculate half the radius.
To find half the radius, we compute:
\[ \frac{r}{2} = \frac{1}{2} \times \frac{88}{\pi} = \frac{88}{2\pi} = \frac{44}{\pi} \]

### Step 5: Substitute the value of \( \pi \).
Using \( \pi \approx \frac{22}{7} \):
\[ \frac{44}{\pi} = \frac{44}{\frac{22}{7}} = 44 \times \frac{7}{22} = 2 \times 7 = 14 \, \text{cm} \]

### Final Answer:
Half the radius of the circle is \( 14 \, \text{cm} \).

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