Question

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

Answer 1

let shorter side be x,
so, longer side is (x+30),
So,diagonal is square root of (x^2+(x+30)^2),
so,square root of(x^2+(x+30)^2)=x+60,
so,after solving we get, 
x=90,-30.
and we know side can't be negative so shorter side = 90 metre and longer one is 120 metre

Answer 2

Solution:

Let us suppose,

the shorter side of the rectangle be x m.

Then, larger side of the rectangle = (x + 30) m

Diagonal of the rectangle = √[x²+(x+30)²]

As given, the length of the diagonal is = x + 60 m

⇒ x² + (x + 30)² = (x + 60)²

⇒ x² + x² + 900 + 60x = x² + 3600 + 120x

⇒ x² – 60x – 2700 = 0

⇒ x² – 90x + 30x – 2700 = 0

⇒ x(x – 90) + 30(x -90)

⇒ (x – 90)(x + 30) = 0

⇒ x = 90, -30

Hence,

The sides of the fields are 90 and -30.