Question

If the length and breadth of a rectangular plot are each increased by $1m$ then the area of the floor is increased by $21$ sq m. If the length is increased by $1m$ and breadth is decreased by $m$, then the area is decreased by $5$ sq m. What is the perimeter of the floor?

• A. $30m$
• B. $32m$
• C. $36m$
• D. $40m$

Answer 1

The correct option is D $40m$

Let the length and breadth of the rectangle be $x$ m and $y$ m, respectively.
Then, $(x+1)(y+1)=xy+21$ ...(i)
$(x+1)(y-1)=xy-5$ ...(ii)
$\Rightarrow xy+y+x+1=xy+21$
$\Rightarrow x+y+1=21$

$\Rightarrow x+y=20$ .....(iii)
and $xy+y-x-1=xy-5$
$\Rightarrow -x+y-1=-5$

$\Rightarrow x-y=4$ ....(iv)
Adding (iii) and (iv) we get,

$2x=24$

$\Rightarrow x=12$
Putting the value of $x$ in (iii), we get

$12+y=20$

$\Rightarrow y=8$
$\therefore$ Perimeter $=2(x+y)=2\times 20=40m$