4. At the rate ₹100 per metre, it will cost the village panchayat ₹75000 to fence the plot.

Let the length of the rectangular plot = $11x$ and the breadth = $4x$.  

Rate of fencing per metre = ₹100  
Total cost of fencing = ₹75,000  

Perimeter of the plot = $2(l + b) = 2(11x + 4x) = 2 \times 15x = 30x$  

Total amount of fencing = $30x \times 100$  

According to the question:

$30x \times 100 = 75000$
$\Rightarrow 3000x = 75000$
$\Rightarrow x = \dfrac{75000}{3000}$
$\Rightarrow x = 25$

Length of the plot = $11x = 11 \times 25 = 275\,\text{m}$  
Breadth of the plot = $4x = 4 \times 25 = 100\,\text{m}$  

Thus, the dimensions of the plot are $275\,\text{m} \times 100\,\text{m}$.

मान लीजिए भू-खण्ड की लंबाई = $11x$ और चौड़ाई = $4x$।  

बाड़ लगाने की दर = ₹100 प्रति मीटर  
कुल खर्च = ₹75,000  

भू-खण्ड का परिमाप = $2(l + b) = 2(11x + 4x) = 2 \times 15x = 30x$  

कुल खर्च = $30x \times 100$  

प्रश्न के अनुसार:

$30x \times 100 = 75000$
$\Rightarrow 3000x = 75000$
$\Rightarrow x = \dfrac{75000}{3000}$
$\Rightarrow x = 25$

भू-खण्ड की लंबाई = $11x = 11 \times 25 = 275\,\text{m}$  
भू-खण्ड की चौड़ाई = $4x = 4 \times 25 = 100\,\text{m}$  

अतः भू-खण्ड का आयाम $275\,\text{m} \times 100\,\text{m}$ है।