Area of a rectangle is 150 sq. metre. When the breadth of the same rectangle is increased by 2 metres and the length decreased by 5 metres the area of the rectangle decreases by 30 square metres. What is the perimeter of the square whose sides are equal to the length of the rectangle ?

Answer: Option D

Let the length of rectangle be $$l$$ metre and the breadth of the rectangle be $$b$$ metre
Then area of the rectangle = $$l$$ × $$b$$
$$lb$$ = 150 m² . . . . . (i)
According to the question,
$$\begin{array}{rl}& \left(l-5\right)\times \left(b+2\right)=150-30\\ & \Rightarrow \left(l-5\right)\times \left(b+2\right)=120\\ & \Rightarrow lb-5b+2l-10=120\\ & \Rightarrow 150-5b+2l-10=120\\ & \Rightarrow 5b-2l=20\\ & \Rightarrow \frac{5\times 150}{l}-2l^2=20l\\ & \Rightarrow 2l^2+20l-750=0\\ & \Rightarrow l^2+10l-375=0\\ & \Rightarrow l\left(l+25\right)-15\left(l+25\right)=0\\ & \Rightarrow \left(l+15\right)\left(l+25\right)=0\end{array}$$
On solving both equations we get,
$$l$$ = 15 m and $$b$$ = 10 m
Side of square = length of rectangle (given)
So, the perimeter of the square :
= 4 × $$l$$
= 4 × 15
= 60 m