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Question

A square is formed by reducing the length of a rectangle by 4 cm and increasing it's width by 3 cm. Both the figures have the same area. Find the perimeter of the original rectangle.



Your Answer
A

48 cm

Correct Answer
B

50 cm

Your Answer
C

40 cm

Your Answer
D

None of these


Solution

The correct option is B

50 cm


Let x and y be the length and breadth of the rectangle respectively.

Then, x – 4 = y + 3 or x – y = 7 ---------- (i)   

Area of the rectangle = x y; Area of the square = (x – 4) (y + 3)

(x – 4) (y + 3) =x y

3x – 4y = 12    ----------- (ii)

Solving (i) and (ii), we get x = 16 and = 9.

 Perimeter of the rectangle = 2 (x + y= [2 (16 + 9)] cm = 50 cm.

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