If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle.

If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle. Correct Answer 50

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 =xy; Area of the square = (x - 4) (y + 3)(x - 4) (y + 3) =xy <=> 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.

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