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The area of a circular field is equal to the area of a rectangular plain whose perimeter is 400 m and the ratio of length and width is 14 : 11. What will be the circumference (in m) of the circular ground? (Take  \(\pi=\dfrac{22}{7}\))
1. 376
2. 432
3. 352
4. 428

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Correct Answer - Option 3 : 352

Given:

The perimeter of the rectangle = 400 metre

The ratio of length and width of rectangle = 14 : 11

The area of the rectangle = area of the circle

Formula used:

Area of a Circle = πr2

Circumference of a Circle = 2πr

Perimeter of a Rectangle = 2 × (length + breadth)

Area of a Rectangle = length × breadth

Calculation:

The perimeter of the rectangle

2(14x + 11x) = 400

⇒ 25x = 200

⇒ x = 8

Lenght = 8 × 14 = 112 m

Breadth = 8 × 11 = 88 m

Area of circle = area of rectangle

⇒ πr2 = 88 × 112

⇒ r2 = 88 × 112 × 7/22

⇒ r2 = 3136

⇒ r= 56 m

Circumference of the circle is

⇒ 2 × (22/7) × 56

⇒ 352 m

∴ The circumference of the circle is 352 metre.

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