Given information:
- Area of the circle = 2464 cm²
- Ratio of the breadth of the rectangle to the radius of the circle = 6:7
- Circumference of the circle = Perimeter of the rectangle

To find: The area of the rectangle

Let's solve the problem step by step:

1. Find the radius of the circle:
- The area of the circle is given as 2464 cm².
- We know that the area of a circle is given by the formula: A = πr², where A is the area and r is the radius.
- Substituting the given area, we have: 2464 = πr²
- Divide both sides by π: r² = 2464/π
- Taking the square root of both sides, we get: r = √(2464/π)

2. Find the breadth of the rectangle:
- The ratio of the breadth of the rectangle to the radius of the circle is given as 6:7.
- Let the breadth of the rectangle be 6x and the radius of the circle be 7x, where x is a constant.
- Since the radius of the circle is 7x, we can substitute this value in the equation obtained in step 1: r = 7x.
- Solve for x: √(2464/π) = 7x
- Divide both sides by 7: x = √(2464/π)/7

3. Find the circumference of the circle:
- The circumference of a circle is given by the formula: C = 2πr, where C is the circumference and r is the radius.
- Substitute the value of the radius obtained in step 2: C = 2π(7x) = 14πx

4. Find the perimeter of the rectangle:
- The perimeter of a rectangle is given by the formula: P = 2(breadth + length), where P is the perimeter, breadth is the breadth of the rectangle, and length is the length of the rectangle.
- Since the ratio of the breadth to the radius is 6:7, the length of the rectangle will be 7x.
- Substitute the values: P = 2(6x + 7x) = 2(13x) = 26x

5. Equate the circumference of the circle and the perimeter of the rectangle:
- From step 3, we have: 14πx = 26x
- Divide both sides by x: 14π = 26
- Divide both sides by 14: π = 26/14 = 13/7

6. Find the area of the rectangle:
- Since the perimeter of the rectangle is equal to the circumference of the circle, we can substitute the value of π obtained in step 5 into the formula for the area of the rectangle: A = length × breadth
- Substitute the values: A = 7x × 6x = 42x²
- Multiply both sides by 7/13 (to cancel out the value of x): A = (42x²) × (7/13) = 294x²/13
- Substitute the value of x obtained in step 2: A = 294(√(2464/π)/7)²/13
- Simpl