The perimeter of a circular park is equal to the perimeter of a rectangular field. If the ratio of the length and breadth of the rectangular field is 3 ∶ 1 and the area of it is 363 m2, then what will be the area of the circular park?

The perimeter of a circular park is equal to the perimeter of a rectangular field. If the ratio of the length and breadth of the rectangular field is 3 ∶ 1 and the area of it is 363 m2, then what will be the area of the circular park? Correct Answer 616

Given:

The perimeter of a circular park is equal to the perimeter of a rectangular field

The ratio of the length and breadth of the rectangle is 3 ∶ 1

The area of the rectangle is 363 m²

Formula used:

The perimeter of a circle = 2πr

The area of a circle = πr²

Where r is the radius of the circle

The area of a rectangle = (Length × Breadth)

The perimeter of a rectangle = 2(Length + Breadth)

Calculation:

Let the length and the breadth be 3x and x respectively

According to the question we can say,

3x² = 363

⇒ x² = 121

⇒ x = 11

So, length = (3 × 11) meters = 33 meters

Breadth = (1 × 11) meters = 11 meters

The perimeter of the rectangular field = 2(33 + 11) meters

⇒ 88 meters

Now, as per the question, we can say

2πr = 88

⇒ r = 14

Now, the area of the circular park = πr²

⇒ πr² = (22/7) × 14²

⇒ 616

∴ The area of the circular park is 616 m²