Question

the length and breadth of a park are in the ratio 3:1 and its perimeter is 320 metre wide runs inside it find the cost of paving the path at rupees 3 square per metre​

Answer 1

hey mate here is ur solution

Answer 2

Correction : The length and breadth of a park in the ratio 3:1 and its perimeter is 320 m. A path 2m wide runs inside it,along its boundary. Find the cost of paving the path at Rs 3 per square metre ?

Solution:

Define x :

Let the length of park and breadth of park be x m .

Given that :

• Length of the park = 3x
• Breadth of the park = x
• Perimeter of the park = 320 m

∵ Perimeter of the Park = 2 ( Length + Breadth)

☞ 320 = 2 ( 3x + x )

☞ 320 = 2 (4x)

☞ 320 = 8x

☞ x = 320/8

☞ x = 40

Therefore, Length of the Park = 3(40) = 120 m

∵ Breadth of the park = x = 40 m

∵ Area of the Park = Length × Breadth

Area of the park = 120 × 40

0r, Area of the Park = 4800 m²

Here, Assume a path of 2m wide runs inside the path along the boundary.

∴ Length of the excluding part = 120 - (2 + 2)

0r, Length of the excluding part = 120 - 4

0r, Length of the excluding Part = 116 m

∴ Breadth of the excluding part = 40 - (2+2)

0r, Breadth of the excluding Part = 36 m

∵ Area of the excluding part of Park = 116 × 36

Area of the excluding part of Park = 4176 m²

Define the area of the path :

Area of the Path = Area of Park - Area of the excluding part of Park

0r, Area of the Path = 4800 m² - 4176 m²

0r, Area of the Path = 624 m²

Find the cost of paving the path at rupees 3 per m².

Cost of paving the path at rupees 3 per m² = Area of the path × Cost of paving the path

Cost of paving the path = 624 × 3

0r, Cost of Paving the path = Rs 1872

Hence, Cost of paving the path at rupees 3 per m² is ₹1872.