To find the length of one side of the base of a square pyramid, we can use the information about the surface area and the area of the triangular faces.
The formula for the surface area \( S \) of a square pyramid can be expressed as:
\[ S = A_b + A_t \]
where:
- \( A_b \) is the area of the base (which is a square),
- \( A_t \) is the total area of the triangular faces.
We are given:
- Total surface area \( S = 65 , \text{ft}^2 \)
- Total area of the four triangular faces \( A_t = 40 , \text{ft}^2 \)
First, we can find the area of the base:
\[ A_b = S - A_t = 65 - 40 = 25 , \text{ft}^2 \]
Since the base is a square, we can express the area of the base in terms of the side length \( s \):
\[ A_b = s^2 \]
Set \( s^2 \) equal to the area we just calculated:
\[ s^2 = 25 \]
Taking the square root of both sides to solve for \( s \):
\[ s = \sqrt{25} = 5 , \text{ft} \]
Thus, the length of one of the sides of the base of the square pyramid is:
\[ \boxed{5 , \text{ft.}} \]