To find the value of \( x \), we start with the formula for the perimeter \( P \) of a rectangle, which is given by:
\[ P = 2(\text{length} + \text{width}) \]
Given that one side length (width) is \( 5x + 14 \) ft and the other side length (length) is \( 5x + 26 \) ft, we can set up the equation for the perimeter:
\[ 230 = 2((5x + 14) + (5x + 26)) \]
First, combine the expressions inside the parentheses:
\[ (5x + 14) + (5x + 26) = 5x + 14 + 5x + 26 = 10x + 40 \]
Now substitute this back into the perimeter equation:
\[ 230 = 2(10x + 40) \]
Next, simplify the equation by distributing the \( 2 \):
\[ 230 = 20x + 80 \]
Now, to isolate \( x \), subtract \( 80 \) from both sides:
\[ 230 - 80 = 20x \ 150 = 20x \]
Now, divide both sides by \( 20 \):
\[ x = \frac{150}{20} \ x = 7.5 \]
Thus, the value of \( x \) is:
\[ \boxed{7.5} \]
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