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

let length = l , breadth = b

l = 3x , b = 2x

perimeter of the rectangular park = distance covered by the man in one round

= 12 $$\times \frac{5}{18}\times 8 \times 60   (\because 1min = 60secs$$ and converting 12km/hr to m/s by multiplying it by $$\frac{5}{18})$$

= 1600 m

2(3x+2x) = 1600

5x= 800

x = 160

l = 3x = 160$$\times$$3 = 480

b = 2x = 160$$\times$$2 = 320

area of the rectangle = $$l \times b$$ = $$480 \times 320$$

=$$ 153600  m^2 $$