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?
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 Perimeter of plot.
Thus equation becomes,
100 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