Let shorter side of rectangle ABCD be x metre, Then, longer side of rectangle ABCD,
AB = (x + 30) m.
Diagonal AC = (x + 60) m.
In ⊥∆ABC, ∠B = 90°.
As per Pythagoras theorem,
AB2 + BC2 = AC2
(x + 30)2 + (x)2 = (x + 60)2
x2 + 60x + 900 + x2 = x2 + 120x + 3600
2x2 + 60x + 900 = x2 + 120x + 3600
2x2 – x2 + 60x – 120x + 900 – 3600 = 0
x2 – 60x – 2700 = 0
x2 – 90x + 30x – 2700 = 0
x(x – 90) + 30 (x – 90) = 0
(x – 90) (x + 30) = 0
If x – 90 = 0, then x = 90
If x + 30 = 0, then x = -30
Shorter side of rectangle, BC = x = 90 m.
Longer side of rectangle, AB = x + 30 = 90 + 30= 120 m.
Diagonal of rectangle, AC = x + 60 = 90 + 60 = 150 m.