The length of a rectangle is thrice its breadth. If its length is decreased by 9 cm and breadth is increased by 9 cm, the area of the rectangle is increased by 81 sq. cm. Find the original length of the rectangle.

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The length of a rectangle is thrice its breadth. If its length is decreased by 9 cm and breadth is increased by 9 cm, the area of the rectangle is increased by 81 sq. cm. Find the original length of the rectangle.