To find the value of \( x \), we start by using the formula for the perimeter of a square, which is given by:
\[ P = 4s \]
where \( s \) is the length of one side of the square.
According to the problem, the perimeter can also be expressed as \( 4x + 20 \) ft. We set this equal to the given perimeter of 96 ft:
\[ 4x + 20 = 96 \]
Now, we need to solve for \( x \). First, we can isolate \( 4x \) by subtracting 20 from both sides:
\[ 4x = 96 - 20 \]
This simplifies to:
\[ 4x = 76 \]
Next, we divide both sides by 4 to solve for \( x \):
\[ x = \frac{76}{4} \]
Calculating this gives:
\[ x = 19 \]
Thus, the value of \( x \) is:
\[ \boxed{19} \]