The ratio of the length and breadth of a rectangular garden is 14: 11 and its perimeter is 800 m. Its area is equal to the area of a circular field. What is the perimeter (in m) of the circular field? (Take π=
7
22
​
)

Let the length and breadth of the rectangular garden be 14x and 11x respectively.
Perimeter of a rectangle =2(length+breadth)

2(14x+11x)=800
2(25x)=800⟹50x=800⟹x=16
So, the dimensions are:

Length=14×16=224 m
Breadth=11×16=176 m
Area of the rectangle =Length×Breadth=224×176 m
2


Given that the area of the circular field equals the area of the rectangle:

πr
2
=224×176
7
22
​
×r
2
=224×176
r
2
=
22
224×176×7
​

r
2
=224×8×7
r
2
=(32×7)×8×7=256×49
r=
256×49

​
=16×7=112 m
Perimeter (circumference) of the circular field:

Perimeter=2πr=2×
7
22
​
×112=2×22×16=704 m