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.

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Solution

## 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. $\therefore 22\mathrm{x}=132\phantom{\rule{0ex}{0ex}}⇒\mathrm{x}=\frac{132}{22}=6\phantom{\rule{0ex}{0ex}}\therefore \mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{field}=\left(7×6\right)\mathrm{m}=42\mathrm{m}\phantom{\rule{0ex}{0ex}}\mathrm{Breadth}\mathrm{of}\mathrm{the}\mathrm{field}=\left(4×6\right)\mathrm{m}=24\mathrm{m}$

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