To find the length of one of the sides of the square pyramid, we can use the information provided about the surface areas.
The surface area \(S\) of a square pyramid is given by the formula: \[ S = B + L \] where \(B\) is the area of the base (which is a square), and \(L\) is the total area of the lateral (triangular) faces.
Here, we are given:
- \(S = 65 , \text{ft}^2\) (the total surface area)
- \(L = 40 , \text{ft}^2\) (the area of the four triangular faces)
We can find the area of the base \(B\): \[ B = S - L = 65 , \text{ft}^2 - 40 , \text{ft}^2 = 25 , \text{ft}^2 \]
Since the base of the pyramid is a square, the area of the base \(B\) can also be expressed in terms of the length of one side \(s\) of the square: \[ B = s^2 \]
Setting this equal to the area we found: \[ s^2 = 25 , \text{ft}^2 \]
Now, we take the square root to find \(s\): \[ s = \sqrt{25 , \text{ft}^2} = 5 , \text{ft} \]
Thus, the length of one of the sides of the square pyramid is: \[ \boxed{5 , \text{ft}} \]