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.

• A. 48 cm
• B. 50 cm
• C. 40 cm
• D. None of these

Answer 1

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)

$\Rightarrow$ (x – 4) (y + 3) =x y

$\Rightarrow$ 3x – 4y = 12 ----------- (ii)

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

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