Question

The length and breadth of a rectangular piece of land are in the ratio of 5 : 3. If the total cost of fencing it at Rs 24 per metre is Rs 9600, find its length and breadth.

Answer 1

Total cost of fencing a rectangular piece = Rs. 9600
Rate of fencing = Rs. 24
∴ Perimeter of the rectangular field = $\left(\frac{\mathrm{Total}\mathrm{cost}\mathrm{of}\mathrm{fencing}}{\mathrm{Rate}\mathrm{of}\mathrm{fencing}}\right)$ m = $\left(\frac{9600}{24}\right)$ m = 400 m

Let the length and breadth of the rectangular field be 5x and 3x, respectively.
Perimeter of the rectangular land = 2(5x + 3x) = 16x
But the perimeter of the given field is 400 m.
∴ 16x = 400
x = $\left(\frac{400}{16}\right)$ = 25
Length of the field = (5 $\times$ 25) m = 125 m
Breadth of the field = (3 $\times$ 25) m = 75 m