Question

The area of a rectangle is $255$ $m^2$. If its length is decreased by $1$ m and its breadth is increased by $1$ m, it becomes a Square. Find the perimeter of the square.

• A. $45m$
• B. $60m$
• C. $55m$
• D. $64m$

Answer 1

Answer: (D)

$64m$

Let length and breadth of rectangle be x & y respectively.
Given that, xy = 255 According to the question, (x - 1)= (y + 1)
So, $(y+2)y=255$
And $y^2$ + $2y-255=0$
$\Rightarrow y^2+17y15y255=0\Rightarrow y(y+17)-15(y+17)=0$
$\Rightarrow (y-15)(y-17)=0\Rightarrow 15$ or y = $-17$
Negative value is discarded.
Hence x = $\frac{255}{y}=\frac{255}{15}$ = $17$
So, side of the square = $(y+1)=15+1=16$
Hence, its perimeter $16\times$ $4=64m$
Alternate Method:
As perimeter of square is $4$ side, the answer should be divisible by $4$. Hence, the
answer can be either $60$ or $64$. By taking the answer choice as $64$, we get the side as $16$ which satisfies the condition in the question.