Question

# The cost of fencing a rectangular field at Rs 30 per metre is Rs 2400. If the length of the field is 24 m, then its breadth is (a) 8 m (b) 16 m (c) 18 m (d) 24 m

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Solution

## (b) 16 m Total cost of fencing = Rs 2400 Rate of fencing = Rs 30/m Perimeter of the rectangular field = $\frac{\mathrm{Total}\mathrm{cost}}{\mathrm{Rate}}=\frac{\mathrm{Rs}2400}{\mathrm{Rs}30/\mathrm{m}}=80\mathrm{m}$ Let the breadth of the rectangular field be x m. Perimeter of the rectangular field = 2(24 + x) m $⇒2\left(24+x\right)=80\phantom{\rule{0ex}{0ex}}⇒48+2x=80\phantom{\rule{0ex}{0ex}}⇒2x=\left(80-48\right)\phantom{\rule{0ex}{0ex}}⇒2x=32\phantom{\rule{0ex}{0ex}}⇒x=\frac{32}{2}=16\phantom{\rule{0ex}{0ex}}\mathrm{So},\mathrm{the}\mathrm{breadth}\mathrm{of}\mathrm{the}\mathrm{rectangular}\mathrm{field}\mathrm{is}16\mathrm{m}.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$

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