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 ?

Solution(By Examveda Team)

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,
$$\eqalign{ & \left( {l - 5} \right) \times \left( {b + 2} \right) = 150 - 30 \cr & \Rightarrow \left( {l - 5} \right) \times \left( {b + 2} \right) = 120 \cr & \Rightarrow lb - 5b + 2l - 10 = 120 \cr & \Rightarrow 150 - 5b + 2l - 10 = 120 \cr & \Rightarrow 5b - 2l = 20 \cr & \Rightarrow \frac{{5 \times 150}}{l} - 2{l^2} = 20l \cr & \Rightarrow 2{l^2} + 20l - 750 = 0 \cr & \Rightarrow {l^2} + 10l - 375 = 0 \cr & \Rightarrow l\left( {l + 25} \right) - 15\left( {l + 25} \right) = 0 \cr & \Rightarrow \left( {l + 15} \right)\left( {l + 25} \right) = 0 \cr} $$
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