Question

The sides of a rectangular park are in the ratio $4:3$. If the area is $1728m$, find the cost of fencing it at the rate of $Rs.2.50/m$

Answer 1

$ABCD$ is a rectangular park
Comsider $AB$ and $BC$ be the sides of the rectangle $AB:BC$ = $4:3$
$\therefore$ let $AB=4x$ and $BC=3x$
Area of rectangle = $l$$\times b$
$4x$ x $3x$ = $1728$
$\Rightarrow 12x^2$ = $1728$
$\Rightarrow x^2$ = $\frac{1728}{2}$
$\Rightarrow x^2$=$144$
$\Rightarrow x$=$\sqrt{144}$ = $12$
Hence Length = $4x$ = $4$ x$12$ = $48m$
Breadth = $3x$ = $3$ x $12$ = $36m$
$\therefore$ Perimeter of a rectangle = $2(l+b)$
$\Rightarrow 2(48+36)$ = $2$ x $84$ = $168m$
Cost of fencing = $perimeter\times Rate=$ $168$ x $2.50$
The total cost of fencing is $Rs.420$