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 ?

Answer: Option D

$$\begin{array}{rl}& 2\left(14x+11x\right)=100\\ & \Rightarrow 25x=50\\ & \Rightarrow x=2\end{array}$$
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,
$$\begin{array}{rl}& \frac{22}{7}\times r^2=616\\ & \Rightarrow r^2=\frac{616\times 7}{22}\\ & \Rightarrow r^2=196\\ & \Rightarrow r=14m\end{array}$$
∴ Diameter :
$$\begin{array}{rl}& =\left(2\times 14\right)m\\ & =28m\end{array}$$