To find the length of each side of the bigger garden, we need to take the square root of the area.
The area of the bigger garden is given as 38.4 m^2. Taking the square root of 38.4 gives us approximately 6.2 m.
Next, we need to decrease the length of each side by 1.7 m to find the length of each side of the smaller garden. So, the length of each side of the smaller garden will be 6.2 m - 1.7 m = 4.5 m.
Now that we know the length of each side of the smaller garden (4.5 m), we can calculate the perimeter by multiplying it by 4 since all sides of a square are equal.
Therefore, the perimeter of the smaller garden is 4.5 m * 4 = 18 m.