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The area of a circular field is equal to the area of a rectangular field. The ratio of the length and the breadth of the rectangular field is 14 : 11 respectively and perimeter is 100 metres. What is the diameter of the circular field ?

The area of a circular field is equal to the area of a rectangular field. The ratio of the length and the breadth of the rectangular field is 14 : 11 respectively and perimeter is 100 metres. What is the diameter of the circular field ? Correct Answer 28 m

$$\eqalign{ & 2\left( {14x + 11x} \right) = 100 \cr & \Rightarrow 25x = 50 \cr & \Rightarrow x = 2 \cr} $$
So, length and breadth of the rectangular field are 28 m and 22 m respectively
Area of the circle = Area of the rectangular field
= (28 × 22) m2
= 616 m2
Let the radius of the circle be r metres
Then,
$$\eqalign{ & \frac{{22}}{7} \times {r^2} = 616 \cr & \Rightarrow {r^2} = \frac{{616 \times 7}}{{22}} \cr & \Rightarrow {r^2} = 196 \cr & \Rightarrow r = 14\,m \cr} $$
∴ Diameter :
$$\eqalign{ & = \left( {2 \times 14} \right)\,m \cr & = 28\,m \cr} $$

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