Step 1 :Given that the gardens are in the shape of regular triangles, the lengths of the sides of the two triangular gardens are 3m and 4.5m respectively.
Step 2 :The perimeter of a regular triangle (equilateral triangle) is simply three times the length of one side.
Step 3 :Calculate the perimeter of the first triangle: \(3 \times 3 = 9\) meters
Step 4 :Calculate the perimeter of the second triangle: \(3 \times 4.5 = 13.5\) meters
Step 5 :Add the perimeters of the two triangles to get the total length of the tile needed: \(9 + 13.5 = 22.5\) meters
Step 6 :Final Answer: The total length of the tile needed is \(\boxed{22.5}\) meters