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 ?
Options:
A . 14 m
B . 22 m
C . 24 m
D . 28 m
E . None of these
Answer: Option D $$\eqalign{ & 2\left( {14x + 11x} \right) = 100 \cr & \Rightarrow 25x = 50 \cr & \Rightarrow x = 2 \cr} $$ 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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