Question

If the area of a rectangular plot is $396\mathrm{sq}.\mathrm{m}$ and its breadth is $18\mathrm{m}$. Find the length of the plot and the cost of fencing it at the rate of ₹$7.50\mathrm{per}\mathrm{metre}.$

Answer 1

Step 1: Find the length of plot.

Given;

Area of rectangular plot is $=$ $396{\mathrm{m}}^2$

Breadth of rectangle is $=$$18\mathrm{m}$

and cost of fencing rectangular plot is $=$ ₹ $7.50\mathrm{per}\mathrm{meter}$

we know that ;

Area of rectangle $=\mathrm{length}\times \mathrm{breadth}$

Therefore,

$\mathrm{length}\times \mathrm{breadth}=396{\mathrm{m}}^2$

$\Rightarrow$ $\mathrm{length}\times 18\mathrm{m}=396{\mathrm{m}}^2$

$\Rightarrow \mathrm{length}=\frac{396}{18}$

$\Rightarrow \mathrm{length}=22\mathrm{m}$

Hence, the length of rectangular plot is $22\mathrm{m}$.

Step 2: Find the cost of fencing plot.

Perimeter of rectangle $=2(\mathrm{length}+\mathrm{breadth})$

Therefore , Perimeter of rectangular plot $=$$2(22+18)$$\mathrm{m}$

Perimeter of rectangular plot $=$$2\times 40=80\mathrm{m}$

Since , the total cost of fencing the rectangular plot is $=$ $\mathrm{Perimeter}\mathrm{of}\mathrm{rectangular}\mathrm{plot}$ $\times \mathrm{cost}\mathrm{of}\mathrm{fencing}\mathrm{per}\mathrm{metre}$

$\Rightarrow$ the total cost of fencing the rectangular plot is $=$ $80\times 7.50$ $=$₹$600.$

Hence, the length the length of rectangular plot is $22\mathrm{m}$

and the total cost of fencing the rectangular plot is ₹$600$.