The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

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