Answer :

**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

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,⇒ x^{2} + (x+30)^{2} = (x+60)^{2}

⇒ x^{2} +x^{2} +900+60x = x^{2}+3600+120x

⇒ x^{2} – 60x – 2700 = 0

⇒ 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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