There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio of $11 : 4$ At the rate of $₹ 100 p e r m e t e r$ it will cost the village panchayat $₹ 75000$ to fence the plot. What are the dimensions of the plot?

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Solution

Step-1: Given Information
The length and breadth of the plot are in the ratio of $11 : 4$
Let the length of the rectangular plot be $11 x$
Let the breadth of the rectangular plot be $4 x$
Rate of fencing per meter = $₹ 100$
The total cost of fencing = $₹ 75000$
Step-2: Find the length or fencing or perimeter of the rectangular plot
$P e r i m e t e r o f t h e p l o t = 2 \times (l + b)$
$P e r i m e t e r o f t h e p l o t = 2 \times (11 x + 4 x)$
$P e r i m e t e r o f t h e p l o t = 2 \times (15 x)$
$P e r i m e t e r o f t h e p l o t = 30 x m$
Step-3: Find the value of $x$
Cost of fencing one meter = $₹ 100$
Cost of fencing of $30 x m = 30 x \times 100 = 3000 x$
and, The total cost of fencing = $₹ 75000$
According to the given details, the equation becomes
$3000 x = 75000$
$x = \frac{75000}{3000}$
$x = 25 m$
Step-4: Find the dimensions of the plot
Length of the plot $= 11 x = 11 \times 25 = 275 m$
The breadth of the plot $= 4 \times 25 = 100 m$
Hence, the Length of the plot $= 275 m$ and the Breadth of the plot $= 100 m$

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