The ratio between the length and breadth of a rectangular park is 3:2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then what is the area of the park (in square meter)?
The ratio between the length and breadth of a rectangular park is 3:2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then what is the area of the park (in square meter)?
Explanation
- 1. The ratio of length to breadth is 3:2. Let's assume the length is 3x and the breadth is 2x.
- 2. The perimeter of the rectangular park is 2(3x + 2x) = 10x.
- 3. The man completes one round in 8 minutes at a speed of 12 km/hr. Convert the speed to meters per minute:
12 km/hr = 12,000 m/60 min = 200 m/min
- 1. The distance covered in 8 minutes is:
200 m/min × 8 min = 1600 m
Since the man completes one round, the perimeter of the park is 1600 m:
10x = 1600
x = 160
Now, find the length and breadth:
Length = 3x = 3 × 160 = 480 m
Breadth = 2x = 2 × 160 = 320 m
Finally, calculate the area:
Area = Length × Breadth = 480 × 320 = 153,600 sq. m