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1. 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 ?

A. 76 m

B. 72 m

C. 120 m

D. 60 m

Solution:

Let the length of rectangle be

l

metre and the breadth of the rectangle be

b

metre
Then area of the rectangle =

l

b

l b

= 150 m² . . . . . (i)
According to the question,

\begin{aligned} (l - 5) \times (b + 2) = 150 - 30 \\ \Rightarrow (l - 5) \times (b + 2) = 120 \\ \Rightarrow l b - 5 b + 2 l - 10 = 120 \\ \Rightarrow 150 - 5 b + 2 l - 10 = 120 \\ \Rightarrow 5 b - 2 l = 20 \\ \Rightarrow \frac{5 \times 150}{l} - 2 l^{2} = 20 l \\ \Rightarrow 2 l^{2} + 20 l - 750 = 0 \\ \Rightarrow l^{2} + 10 l - 375 = 0 \\ \Rightarrow l (l + 25) - 15 (l + 25) = 0 \\ \Rightarrow (l + 15) (l + 25) = 0 \end{aligned}

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

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