# The diagonal of a

To find:  length and breadth of the field
Let the shorter side of the rectangle be x m.

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

we know,
By pythagoras theorem,
(Hypotenuse)2 = (Base)2 + (Perpendicular)2
Diagonal of a rectangle is √[(length)2 + (breadth)2]

Diagonal of the rectangle =

It is given that the diagonal of the rectangle is 60 m more than the shorter side.

= x+60

Squaring both sides, we get,

⇒ x2 + (x+30)2 = (x+60)2

⇒ x2 +x2 +900+60x = x2+3600+120x

⇒ x2 – 60x – 2700 = 0

Now for solving this quadratic equation, we need to factorize 60 in such a way that the product is 2700 and the difference is 60

⇒ x(x – 90 )+30(x – 90 ) = 0

⇒ (x - 90)(x+30) = 0

⇒ x = 90, -30

However, side cannot be negative. Therefore, the length of the shorter side will be 90 m.

Hence, length of the larger side will be (90 + 30) m = 120 m

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