Question

The perimeter of a rectangle is $40m$. Its length is four meters less than five times its breadth. Find the area of the rectangle.

Answer 1

Let breadth of the rectangle $=x$
Then, length of the rectangle $=5x-4$
We know that,
Perimeter of rectangle $=2(l+b)$
$\Rightarrow 40=2(l+b)[\because$ perimeter = 40 m, given]
$\Rightarrow 40=2(5x-4+x)$
$\Rightarrow 40=2(6x-4)$
$\Rightarrow 12x-8=40$
$\Rightarrow 12x=40+8$
$\Rightarrow 12x=48$
$\Rightarrow x=\frac{48}{12}=4$
So, breadth $=x=4$ and

length $=5x-4=(5\times 4)-4=16m$
$\because$ Area of rectangle = $l\times b=4m\times 16m=64m^2$
Hence, the area of rectangle is $64m^2.$