Let the smaller side = x m
Therefore, hypotenuse = x + 60 m
So, the longer side = x + 30 m
According to the question, (x + 60)² = x² + (x + 30)²
⇒ x² + 120x +3600 = x² + x² + 60x + 900
⇒ – x² + 60x + 2700 = 0
⇒ x² – 60 – 2700 = 0
⇒ x² – 90 + 30x – 2700 = 0
⇒ x(x – 90) + 30 (x – 90) = 0
⇒ (x – 90) (x + 30) = 0
⇒ (x – 90) = 0 or ( x + 30 ) = 0
Either x = 90 or x = – 30
But, x ≠ – 30 ,as x is side of field which can’t be negative.
Therefore, x = 90 and hence the smaller side = 90 m
So, the longer side = 90 + 30 = 120 m