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

#### Solution

Let the common ratio between the length and breadth of the rectangular plot be *x*. Hence, the length and breadth of the rectangular plot will be 11*x* m and 4*x* m respectively.

Perimeter of the plot = 2(Length + Breadth) = `[2(11x + 4x)]m = 30x m`

It is given that the cost of fencing the plot at the rate of Rs 100 per metre is Rs 75, 000.

∴ 100 × Perimeter = 75000

100 × 30x = 75000

3000x = 75000

Dividing both sides by 3000, we obtain

x = 25

Length = 11x m = (11 × 25) m = 275 m

Breadth = 4x m = (4 × 25) m = 100 m

Hence, the dimensions of the plot are 275 m and 100 m respectively.