Q23 of 51 Page 2

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 75000 to fence the plot. What are the dimensions of the plot?

Let the length and breadth of the plot be l = 11 x and b = 4 x respectively.

Since the plot is of rectangular shape and we know  the perimeter of a rectangle is 2(l + b)

Also, rate of fencing the plot is Rs 100 for 1m

Now,

Perimeter of Rectangular plot = 2(l + b) = 2 (11 x + 4 x)

Perimeter of rectangular plot =  2(15 x) = 30 x

Cost of fencing one meter = Rs. 100

Therefore cost of fencing 30 x m = 30 x × 100 = 75000

3000 x = 75000

x = 25

Thus, the length = 11 x (25) = 275 m

And the breadth = 4 x (25) = 100 m

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