The length and breadth of a rectangular plot are in the ratio $ 11: 4$. The cost of fencing the plot with the barbed wire is $₹ 18000$ at the rate of $₹ 100$ per metre. What are the dimensions of the plot?

Given :

The length and breadth of a rectangular plot are in the ratio $11:4$.

The cost of fencing the plot with the barbed wire is Rs. 18000 at the rate of Rs. 100 per metre.

To find :

We have to find the dimensions of the plot.

Solution :

Let the length and breadth of the plot be $11x$ and $4x$ respectively.

This implies,

Total length of the barbed wire $= \frac{18000}{100} = 180 m$.

Perimeter of the rectangle $= 2(11x+4x)$

This implies,

$180 = 2(15x)$

$180 = 30x$

$x = \frac{180}{30}$

$x = 6$

The length of the rectangular plot $= 11(6) = 66 m$.

The breadth of the rectangular plot $= 4(6) = 24 m$.