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To find the perimeter of the lawn, we need to add up all the sides.
Given that the width of the lawn is 3x meters, this means that the length of the lawn must be (15x^2 + 45x) / 3x = 5x + 15 meters.
The perimeter is then calculated as P = 2(Length + Width) = 2(5x + 15 + 3x) = 2(8x + 15) = 16x + 30 meters.
Therefore, the simplified expression to represent the perimeter of the lawn is 16x + 30 meters.