If the ratio of length and breadth of a rectangular park is 5 : 7.  If a man cycling along the boundary of the park at a speed of 18 km/h completes one round in 20 minutes, then area of the park is?

21,87,500 m²

Speed of man = 15 km/hr =18 × \(\frac{5}{18}\) = 5 m/sec

Time taken by man to complete round of the park = 20 min = 1200 sec

Perimeter of the park = Length of one round = speed × time

                                  = (5 × 1200) = 6000 m

Length : Breadth = 5 : 7

Perimeter = 2( L + B) = 24R

⇒ 6000 = 24R

⇒ R = 250

∴ sides of park = 7 × 250, 5 × 250 = 1750 m, 1250 m

Area of park = 1250 × 1750 = 21,87,500 m²