Question

The length and breadth of a park are in the ratio 2: 1 and its perimeter is 240 m. A path 2 m wide runs inside it, along its boundary. Find the cost of paving the path at ₹ 80 per m².

Answer 1

Let us assume the length of the park be 2x

Let us assume the breadth of the park be x

From the question is given that,

Perimeter of the park = 240 m

Wide of the path = 2 m

Rate of paving the path = ₹ 80 per m²

Then,

Perimeter of the park = 2 (l + b) = 240

= 2 (2x + 1x) = 240

= 2 (3x) = 240

= 6x = 240

= x = 240 /6

= x = 40

Then,

The length of the park be 2x = 2 × 40 = 80 m

The breadth of the park be x = 40 m

Let PQRS be the given park and ABCD be the inside boundary of the path.

Area of the park PQRS = (l × b)

= (80 × 40)

= 3200 m²

Wide of the path = 2 m

Then,

AB = (80 – (2 × 2)) = (80 – 4) = 76 m

AD = (40 – (2 × 2)) = (40 – 4) = 36 m

∴Area of the rectangle ABCD = (76 × 36) m² = 2736 m²

Area of the path = (Area of PQRS – Area of ABCD)

= (3200 – 2736)

= 464m²

Rate of paving the path = ₹ 80 per m²

∴Total cost of paving the path of a park = ₹ (80 × 464)

= ₹ 37120