Question

The perimeter of a rectangular field is $140m$. If the length of the field is increased by $2m$ and its breadth decreased by $3m$, the area of the field is increased by $66$ sq. metres. Find the length and breadth of the field.

Answer 1

Let the length and breadth of rectangular field be l and b respectively

$\therefore 2(l+b)=140m\Rightarrow l+b=70\Rightarrow l=70-b⟶\left(1\right)$

Area = $l\times b$ $m^2$

New length $=(l+2)$m, New breadth $=(b-3)$m

New area $=(l+2)(b-3)=lb+2b-3l-6$

$\Rightarrow lb+66=lb+2b-3l-6\Rightarrow 2b-3l=72$

$\Rightarrow 2b-3(70-b)=72\Rightarrow 2b-210+3b=72\Rightarrow 5b=282$

$\Rightarrow b=56.40m$, then $l=70-b=70-56.40=13.60m$

Hence length and breadth are $13.60$m and $56.40$m respectively.