To find the length of one of the sides of the square pyramid, we can use the information given about the surface area and the area of the triangular faces.
The surface area (SA) of a square pyramid is given by the formula:
\[ SA = B + L \]
where \(B\) is the area of the base and \(L\) is the lateral surface area (the area of the triangular faces).
From the problem, we have:
- Total Surface Area (SA) = 65 ft²
- Lateral Area (L) = Area of the four triangular faces = 40 ft²
Now we can find the area of the base \(B\) by rearranging the formula:
\[ B = SA - L \]
Substituting the values:
\[ B = 65 , \text{ft}² - 40 , \text{ft}² = 25 , \text{ft}² \]
Since the base of the pyramid is a square, the area \(B\) can be expressed in terms of the side length \(s\):
\[ B = s^2 \]
Setting this equal to the area we calculated:
\[ s^2 = 25 , \text{ft}² \]
Now, take the square root of both sides to find \(s\):
\[ s = \sqrt{25} = 5 , \text{ft} \]
Thus, the length of one of the sides of the square pyramid is \(5 , \text{ft}\).
So, the answer is 5 ft.