Let’s consider the length of smaller side of rectangle as x metres
Then, the larger side will be (x + 30) metres and diagonal will be = (x + 60) metre
[From given relation]
Now, by using Pythagoras theorem we have,
x2 + (x + 30)2 = (x + 60)2
x2 + x2 + 60x + 900 = x2 + 120x + 3600
2x2 + 60x + 900 – x2 – 120x – 3600 = 0
x2 – 60x – 2700 = 0
x2 – 90x + 30x – 2700 = 0 [By factorisation method]
x(x – 90) + 30(x – 90) = 0
(x – 90)(x + 30) = 0
x = 90 or x = -30 (this is neglected as the side of a rectangle can never be negative)
Therefore, we only take x = 90,
⇒ x + 30 = 90 + 30 = 120
Thus, the length of smaller side of rectangle is 90 metres and the larger side is 120 metres.