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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.