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There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11:4. At the rate ₹100 per metre it will cost the village panchayat ₹75000 to fence the plot.

Q.6 There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11:4. At the rate ₹100 per metre it will cost the village panchayat ₹75000 to fence the plot. What are the dimensions of the plot?

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Let the lenght and breadth of the plot be 11x and 4x repectively.

(Since they are in the ratio11:4)

We know that the fencing will be done on the boundary of the plot, so we need to calculate its perimeter.

Perimeter of rectangle = 2(lenght + breadth)

Total cost to fence the plot = Rs.75000 = Rs.100 \times Perimeter of plot.

Thus equation becomes,

                          100 \times 2(11x + 4x) = 75000

or                       200(15x) = 75000

or                           3000x = 75000

Dividing both sides by 3000:

                              x = 25

Hence lenght of plot is 11x =  275 m

and breadth of the plot is 4x = 100m 

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