Answer :

Let the breadth of the ground be b

Diagonal = b + 60

Length = b + 30

Using Pythagoras theorem

(length)^{2} + (breadth)^{2} = (diagonal)^{2}

⇒ (b + 30)^{2} + b^{2} = (b + 60)^{2}

⇒ (b + 30)^{2} – (b + 60)^{2} = – b^{2}

Using identity (a + b)(a – b) = a^{2} – b^{2}

⇒ (b + 30 + b + 60)(b + 30 – b – 60) = – b^{2}

⇒ (2b + 90)(– 30) = – b^{2}

⇒ b^{2} – 60b – 2700 = 0

⇒ __b ^{2} – 90b__ +

__30b – 2700__= 0

taking b common from first two terms and 30 common from next two

⇒ b(b – 90) + 30(b – 90) = 0

⇒ (b + 30)(b – 90) = 0

⇒ (b + 30) = 0 or (b – 90) = 0

Thus b = 90 m as b cannot be negative because b represents breadth of rectangle

Length = b + 30 = 90 + 30 = 120 m

Area = length × breadth = 120 × 90 = 10800 m^{2}

Therefore, area of ground is 10800 m^{2}

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