The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/h completes one round in 8 minutes, find the area of the park in square metres.

Correct option is D

Given:
Ratio of length to breadth = 3:2
Cycling speed = 12 km/h
Time to complete one round = 8 minutes

Formula Used:
Perimeter of the rectangle = 2 × (length + breadth)
Speed = Distance / Time
Area = Length × Breadth

Solution:
Speed = 12 km/h = 12000 m in 60 minutes
In 8 minutes, the distance traveled = (12000/60) × 8 = 1600 m
Perimeter = 1600 m
Let the length be 3x and breadth be 2x. Then,
2 × (3x + 2x) = 1600
5x = 800
x = 160
Length = 3x = 480 m, Breadth = 2x = 320 m
Area = 480 × 320 = 153600 m²
Thus, the area of the park is 153600 m².