Question

The cost of fencing a rectangular field at Rs 18 per metre is Rs 1980. If the width of the field is 23 m, find its length.

Answer 1

Total cost of fencing = Rs 1980
Rate of fencing = Rs 18 per metre

Perimeter of the field = $\frac{\mathrm{Total}\mathrm{cost}}{\mathrm{Rate}}=\frac{\mathrm{Rs}1980}{\mathrm{Rs}18/\mathrm{m}}=\left(\frac{1980}{18}\right)\mathrm{m}=110\mathrm{m}$

Let the length of the field be x metre.
Perimeter of the field = 2(x + 23) m

$$\begin{gathered} \therefore 2(x+23)=110 \\ \Rightarrow (x+23)=55 \\ x=(55-23)=32 \end{gathered}$$
Hence, the length of the field is 32 m.