Question

The length and the breadth of a rectangular field are in the ratio 7 : 4. The cost of fencing the field at Rs 25 per metre is Rs 3300. Find the dimensions of the field.

Answer 1

Total cost of fencing = Rs 3300
Rate of fencing = Rs 25/m
Perimeter of the field = $\frac{\mathrm{Total}\mathrm{cost}}{\mathrm{Rate}\mathrm{of}\mathrm{fencing}}=\left(\frac{\mathrm{Rs}3300}{\mathrm{Rs}25/\mathrm{m}}\right)=\frac{3300}{25}\mathrm{m}=132\mathrm{m}$

Let the length and the breadth of the rectangular field be 7x and 4x, respectively.
Perimeter of the field = 2(7x + 4x) = 22x

It is given that the perimeter of the field is 132 m.

$$\begin{gathered} \therefore 22\mathrm{x}=132 \\ \Rightarrow \mathrm{x}=\frac{132}{22}=6 \\ \therefore \mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{field}=(7\times 6)\mathrm{m}=42\mathrm{m} \\ \mathrm{Breadth}\mathrm{of}\mathrm{the}\mathrm{field}=(4\times 6)\mathrm{m}=24\mathrm{m} \end{gathered}$$