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 of Rs. 100 per meter, it will cost the village panchayat Rs. 75,000 to fence the plot. What are the dimensions of the plot?

Let the length of the rectangular plot be 11x meters and the breadth be 4x meters.
The perimeter of the rectangular plot is given by 2(length + breadth) = 2(11x + 4x) = 30x meters.
The cost of fencing the plot is Rs. 75,000 at the rate of Rs. 100 per meter.
Therefore, the total length of the fence is 75000 / 100 = 750 meters.
So, we have the equation:
30x = 750
x = 750 / 30
x = 25
Therefore, the length of the plot is 11x = 11 * 25 = 275 meters, and the breadth of the plot is 4x = 4 * 25 = 100 meters.
The dimensions of the plot are 275 meters by 100 meters.