Question

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

Answer 1

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.