From the question we have,
Area of the rectangular field = 3584 m2
Length of the rectangular field = 64 m
Boy runs around the field at the rate = 6 km/h
= ((6 × 1000) / 60) m/min
= 100 m/min
Breadth of the rectangular field = (area /length)
= (3584/ 64)
= 56 m
∴perimeter of the field = 2(l + b) units
= 2 (64 + 56)
= 2 (120)
= 240m
Total distance covered by the boy = 5 × perimeter of the field
= 5 × 240
= 1200m
∴required time to cover the distance of 1200m = (1200/100) = 12min
Hence, boy took 12 min to go 5 times around of rectangular field.