Question

the length and breadth of a park are in the ratio 2 : 1 and its perimeter is 240 M A path 2 metre wide runs inside it along its boundary find the cost of paving the path at rupees 80 per metre square

Answer 1

Answer:

The cost of paving the path is Rs 37,120.

Step-by-step explanation:

It is given that the length and breadth of a park are in the ratio 2 : 1 and its perimeter is 240 m.

We know, length is the longest side, it can't be smaller than any other side.

So,

Let the length of the park be 2 a,

           breadth of the park be a,

We know( formula ),

Perimeter of the rectangle = 2( length + breadth )

In the question, perimeter of the park is 240 m. Therefore : -

= >  2( 2a + a ) = 240 m

= >  2a + a = 240 m / 2

= >  3a = 120 m

= >  a = 120 / 3 m

= >  a = 40 m

Therefore,

Length of the park = 2a = 2( 40 m ) = 80 m

Breadth of the park = a = 40 m

Also, it is given that a path 2 metre wide runs inside it along its boundary.

So,

Length of the path = 2a - 2 - 2 m = 2a - 4 m

            ⇒ 2( 40 ) - 4 m

            ⇒ 80 - 4 m

            ⇒ 76 m

Breadth of the path = a - 2 - 2 m = a - 4 m

           ⇒ 40 - 4 m

           ⇒ 36 m

Now,

Area covered under the path = 76 m x 36 m = 2,736 m^2

Hence,

Area between path the boundaries of park = area of park - area under path

    ⇒ ( 80 x 40 ) m^2 - 2,736 m^2

    ⇒ 3200 m^2 - 2,736 m^2

    ⇒ 464 m^2

Then,

Cost of paving the area under path = rate of paving x area to be paved

           ⇒ Rs 80 / m^2 x 464 m^2

           ⇒ Rs 80 x 464

           ⇒ Rs 37,120

Therefore the cost of paving the path is Rs 37,120.