The diagonal of a rectangular ground is 60 meters more than the breadth of the ground. If the length of the ground is 30 meters more than the breadth, find the area of the ground.

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 + b² = (b + 60)²

⇒ (b + 30)² – (b + 60)² = – b²

Using identity (a + b)(a – b) = a² – b²

⇒ (b + 30 + b + 60)(b + 30 – b – 60) = – b²

⇒ (2b + 90)(– 30) = – b²

⇒ b² – 60b – 2700 = 0

⇒ b² – 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 m²

Therefore, area of ground is 10800 m²