The diagonal of a rectangular field is 60 meters more than the shorter

1.	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» 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.

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»

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.