Question

the length and breadth of a park are in the ratio 3:1 and its perimeter is 320 a path 2 metre wide runs inside it find the cost of paving the birth at rupees 3 square per metre​

Answer 1

$\textbf{\underline{\underline{Answer :-}}}$

The Cost of Paving the path is Rs.1872

$\textbf{\underline{\underline{Explanation :-}}}$

$\textsf{\underline{\underline{Given : }}}$

The ratio of Length to Breadth of Rectangle = 3 : 1

Perimeter of the Rectangle = 320

Path = 2 m wide

Rate of paving the path = Rs.3 sq.m

$\textsf{\underline{\underline{To find :}}}$

The cost of paving the path

$\textsf{\underline{\underline{Solution :}}}$

First we need to find the measure of the sides.

Consider the Length as 3x

Consider the Breadth as 1x (x)

$\star$ As We know :

Perimeter of Rectangle = $\boxed{\sf{2(Length + Breadth)}}$

$\tt{\implies} \:2(3x + x) = 320 \\ \tt{\implies} \:6x + 2x = 320 \\ \tt{\implies} \: 8x = 320 \\ \tt{\implies} \: x = \frac{320}{8} \\ \tt{\implies} \: x = 40$

Value of 3x

$\implies$ 3 × 40

$\implies$ 120

Length = 120

Breadth = 40

$\rule{300}{1}$

Area of the path = Area of Rectangle including path - Area of the Rectangle excluding path.

Area of the Rectangle including path =

$\implies$ 120 × 40

$\implies$ 4800

Area of the Rectangle excluding path =

Length = 120 - (2+2)= 116

Breadth = 40 - (2+2) = 36

$\implies$ 116 × 36

$\implies$ 4176

Area of the path =

$\implies$ 4800 - 4176

$\implies$ 624

Cost of Paving the path =

$\implies$ 624 × 3

$\implies$ 1872

$\therefore$ The Cost of Paving the path is Rs. 1872

Answer 2

Given,

ratio of length and breadth of a park = 3:1

Perimeter of the park = 2(l + b ) = 320

let the each ratio be 3:1

According to the problem,

2(3x + x ) = 320

4x = 320/2

4x = 160

x = 160/4

x = 40

Breadth = x = 40

length = 3x = 120

Area of the park :

= l × b

= 120 × 40

= 4800sq m

When the path goes inside the park then it Subtracts 4 metres from the length and breadth.

breadth = 40 - 4 = 36

length = 120 - 4 = 116

Area of this :

= 116 × 36

= 4176 sq m

Area of the path : Area of total park - Area of inner park

= 4800 - 4176

= 624 sq m

Therefore, the area of the path is 624 sq m.

The cost of paving for one metre = ₹ 3

Then the cost of paving for 624 sq m :

= 624 × 3

= 1872

Therefore, the cost of paving = ₹ 1872