Question
A rectangular grassy plot is $75m$ long and $60m$ broad. If has path of width $2m$ all around it on the inside. Find the area of the path and cost and of constructing it at $Rs 125$ per $m^2$.
✓
Answer
Outer length of plot $(L) = 75m$ and breadth $(B) = 60m$ Width of path inside $= 2m$
Inner length $(l)=75-2 \times 2=75-4=71 \mathrm{~m}$
and width (b) $=60-2 \times 2=60-4=56 \mathrm{~m}$
Area of the path $=\mathrm{L} \times \mathrm{B}-\mathrm{l} \times \mathrm{b}=(75 \times 60-71 \times 56) \mathrm{m}^2=4500-3976=524 \mathrm{~m}^2$
Rate of constructing it $= Rs. 125$ per $\mathrm{m}^2$
Total cost $=$ Rs. $524 \times 125=$ Rs. 65500
Inner length $(l)=75-2 \times 2=75-4=71 \mathrm{~m}$
and width (b) $=60-2 \times 2=60-4=56 \mathrm{~m}$
Area of the path $=\mathrm{L} \times \mathrm{B}-\mathrm{l} \times \mathrm{b}=(75 \times 60-71 \times 56) \mathrm{m}^2=4500-3976=524 \mathrm{~m}^2$
Rate of constructing it $= Rs. 125$ per $\mathrm{m}^2$
Total cost $=$ Rs. $524 \times 125=$ Rs. 65500
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