Let the breadth of the rectangle be "b".
The length of the rectangle is twice the breadth, so it's "2b".
The perimeter of the rectangle is 2x(b+2b) =6b.
The wire bent in the form of a circle also has a circumference of 6b.
Let "r" be the radius of the circle, that is,
2πr=6b, implies, r= 6b/2π
The area of the rectangle is 2b², and the area of the circle is 9b².
So, according to the question, we have,
Area of the circle - Area of the rectangle = 104.5
9b² - 2b² = 104.5
7b² = 104.5
b² = 104.5 / 7
b² = 14.93
b ≈ √14.93 = 3.86
The total length of the wire used is equal to the perimeter of the rectangle:
Total length of wire = 6b
= 6 × 3.86
= 23.16
Therefore, the length of the wire is approximately 23.16 cm.