Let the length of the plot be \( 11x \) meters and the breadth be \( 4x \) meters, according to the given ratio of 11:4.
To find the perimeter \( P \) of the rectangular plot, we can use the formula:
\[ P = 2 \times (\text{Length} + \text{Breadth}) = 2 \times (11x + 4x) = 2 \times 15x = 30x \]
The cost to fence the plot is given as Rs 100 per meter, and the total cost is Rs 75000. Thus, we can relate the perimeter to the cost:
\[ \text{Total Cost} = \text{Perimeter} \times \text{Cost per meter} \]
Substituting the values we have:
\[ 75000 = 30x \times 100 \]
Now simplifying:
\[ 75000 = 3000x \]
Now, divide both sides by 3000 to find \( x \):
\[ x = \frac{75000}{3000} = 25 \]
Now we can find the dimensions of the plot.
- Length \( = 11x = 11 \times 25 = 275 \) meters
- Breadth \( = 4x = 4 \times 25 = 100 \) meters
Therefore, the dimensions of the plot are:
- Length: 275 meters
- Breadth: 100 meters