A man took 20 seconds to cross a rectangular field diagonally, walking at the rate of 54 m/min, and another took the same time to cross the same field along its sides, walking at the rate of 63 m/min. The area of the field is

Let the length = l m and breadth = b m.

So, the length of diagonal = 54*20/60 = 18 m,

Then, l² + b² = 18²,

l² + b² = 324 ----------------------------------(1)

Total distance covered with the rate 63 m/min along with its sides = 

l + b = 63*20/60 = 21,

l + b = 21

On squaring both sides,

l² + b² + 2lb = 441 ---------------------------(2),

On solving equation 1 and 2,

2lb = 117

lb = 58.5

So, area of the field = 58.5 m².