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 shorter side be x m
Then diagonal will be x + 60 m
The longer side will be x + 30 m
By Pythagoras theorem,
(x + 60)² = x² + (x + 30)²
⇒ x² + 3600 + 120x = x² + x² + 900 + 60x
⇒ x² + 120x + 3600 = 2x² + 60x + 900
⇒ 2x² - x² + 60x - 120x + 900 - 3600 = 0
⇒ x² - 60x - 2700 = 0
⇒ (x - 90)(x + 30) = 0
⇒ x = 90, -30
Neglecting negative value, we get x = 90
Shorter Side = 90 m
And longer Side x + 30 = 90 + 30 = 120 m
The shorter side is 90 m and the longer side is 120 m.