Question

The area of a small rectangular plot is $84m^2$. If the difference between its length and the breadth is 5 m; find its pereimeter.

Answer 1

Area of a rectangular plot $=84m^2$

Let breadth =x m

Then length =(x+5) m

$\therefore$ Area $=l\times b$

$\therefore x(x+5)=84$

$x^2+5x-84=0$

$\Rightarrow x^2+12x-7x-84=0$

$\Rightarrow x(x+12)-7(x+12)=0$

$\Rightarrow (x+12)(x-7)=0$

Either x+12=0, then x =-12 which is not possible being negative or x-7=0, then x=7

$\therefore$ Length =x+5=7+5=12 m and breadth =x=7 m

$\therefore$Perimeter =2(l+b)

$=2(12+7)=2\times 19m=38m$