The length and breadth of a park 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 Rs 80 per m².

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Solution

Let the length and the breadth of the park be 2x m and x m, respectively.
Perimeter of the park = 2(2x + x) = 240 m
⇒ 2(2x + x) = 240
⇒ 6x = 240
⇒ x = $(\frac{240}{6})$ m =40 m
∴ Length of the park = 2x = (2 $\times$ 40) = 80 m
Breadth = x = 40 m
Let PQRS be the given park and ABCD be the inside boundary of the path.

Length = 80 m
Breadth = 40 m
Area of the park = (80 $\times$ 40) m² = 3200 m²
Width of the path = 2 m
∴ AB = (80 - 2 $\times$ 2) m = (80 - 4) m =76 m
AD = (40 - 2 $\times$ 2) m = (40 - 4) m = 36 m
Area of the rectangle ABCD = (76 $\times$ 36) m² = 2736 m²
Area of the path = (Area of PQRS - Area of ABCD)
= (3200 - 2736) m² = 464 m²
Rate of paving the path = Rs. 80 per m²
∴ Total cost of paving the path = Rs. (464 $\times$ 80) = Rs. 37,120

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The length and breadth of a park 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 Rs 80 per m2.

The length and breadth of a park 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 Rs 80 per m².