Question

The perimeter of a square plot = 360 m. Find:
i. its area
ii. cost of fencing its boundary at the rate of $Rs.40$ per meter
iii. cost of levelling the plot at $Rs.60$ per square meter.
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Answer 1

The perimeter of the square plot is given by:
$P=4\left(\text{side}\right)$
$\Rightarrow 360=4\left(\text{side}\right)$
$\Rightarrow \text{side}=\frac{360}{4}=90m$
Therefore, the length of each side of the given square is $90m$.

The area of the square plot is given by:
Area$=(side{)}^2=90\times 90=8100m^2$
Therefore, the area of the square plot is $8100m^2$.

Given,
The perimeter of the square plot $=360m$
Rate of fencing the boundary $=Rs.40$ per$m$
Now,
Cost of fencing
$=\text{Perimeter}\times \text{Rate of fencing}$
Therefore,
The cost of fencing $=360\times 40=Rs.14,400$
Hence, the cost of fencing the plot is
$Rs.14,400$.

Given,
Area $=8100m^2$
Cost of levelling $=Rs.60$ per square meter.
Cost of leveling the plot
$=\text{Area}\times \text{Rate of leveling}$
$=8100\times 60=Rs.486000$
Therefore, the cost of leveling the plot is $Rs.4,86,000$.