the length and breadth of a park are in the ratio 2:1 and its perimeter is 240m .a path of 2m wide runs inside it along its boundaries. find the cost of paving the path at rupees 4 per m²
Answers
Answer:
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
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
Answer:
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