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There is a narrow rectangular plot. 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. What are the dimensions of the plot?

There is a narrow rectangular plot. 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. What are the dimensions of the plot?

 

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5962 Points
11 months ago
Dear Student


Let the common ratio be x.

Thus, the length and breadth of a rectangular plot be 11x and 4x.

We know that perimeter of rectangal = 2(length + breadth)

Therefore, the perimeter of the plot here is:

= 2(11x + 4x)

= 2(15x)

= 30x.

Given that Cost of fencing the plot at the rate of rs.100 per metre is 75000.

⇒ 100×Perimeter = 75000

⇒ 100×30x = 75000

⇒ 3000x = 75000

⇒ x = 25

So,

Length of rectangular plot = 11x = 275m

Breadth of rectangular plot = 4x = 100m

Thus, the dimensions of the rectangular plot are 100m and 275m .

Thanks

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