To find the value of \( x \) when the perimeter of the square is given as \( 4X + 26 \) feet and it is also stated that the perimeter is 120 feet, we can set up the following equation:
\[ 4X + 26 = 120 \]
Now, we can solve for \( X \):
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Subtract 26 from both sides: \[ 4X = 120 - 26 \] \[ 4X = 94 \]
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Now, divide both sides by 4: \[ X = \frac{94}{4} \] \[ X = 23.5 \]
Thus, the value of \( X \) is \( 23.5 \).