a wire is bent in the form of a rectangle having length twice the breadth the same wire is bent in the form of a circle it was found that the area of the circle is greater than that of the rectangle by 10 4.5 CM square find the length of the wire
Answers
Answered by
1
A rectangle having a length 2x and breadth x has a perimeter of 6x and an area of 2x2.
A circle having a circumference 6x has a radius of 6x2π=3xπ and an area of π(3xπ)2=9πx2
Since the area of the circle is greater than that of the square by 104.5
9πx2=2x2+104.5
9πx2−2x2=104.5
x2=104.59π−2=120.8387
∴x=10.99
The length of the rectangle is 2×10.99=21.98 cm
and the length of the wire is 6×10.99=65.94 cm
Answered by
2
65.94 cm is the length of the wire
Similar questions