Verified answer

Answer:

• Length of the rectangular plot = 275 m
• Breadth of the rectangular plot = 100 m

Step-by-step explanation:

Given :

• The length and breadth of the plot are in the ratio of 11 : 4.
• At the rate of Rs. 100 per meter it will cost the village panchayat Rs. 75000 to fence the plot.

To find :

the dimensions of the plot

Solution :

Let the length of the plot be 11x and breadth be 4x.

Perimeter of the rectangle = 2(length + breadth)

⇒ P = 2(11x + 4x)

⇒ P = 2(15x)

⇒ P = 30x

It's also given that the cost of fencing is Rs 75000 at the rate of Rs. 100 per meter.

So,

Perimeter of the plot × 100 = 75000

 (30x) (100) = 75000

  3000x = 75000

  x = 75000/3000

  x = 75/3

  x = 25

Therefore,

• Length of the rectangular plot = 11 × 25 = 275 m
• Breadth of the rectangular plot = 4 × 25 = 100 m

Solving in as short as possible:

Let length = 11x

breadth = 4x

Total cost of fencing the rectangular plot = rate of fencing × perimeter

=> 75000 = 100 × 2(l+b)

=> 100 × 2(11x + 4x) = 75000

=> 3000x = 75000

=> x = 75000/3000 = 25

Dimensions are:

Length = 11×25 = 275m

Breadth = 4×25 = 100m

Dimension of the plot = 275m × 100m