To find the value of \( x \), we can use the formula for the perimeter of a rectangle, which is given by:
\[ P = 2(\text{length} + \text{width}) \]
In this case, the length \( L \) is \( 5X + 17 \) feet and the width \( W \) is \( 3X + 21 \) feet.
We know the perimeter \( P \) is 196 feet, so we can set up the equation:
\[ 2((5X + 17) + (3X + 21)) = 196 \]
First, simplify the expression inside the parentheses:
\[ (5X + 17) + (3X + 21) = 5X + 3X + 17 + 21 = 8X + 38 \]
Now substitute this back into the perimeter equation:
\[ 2(8X + 38) = 196 \]
Next, divide both sides by 2:
\[ 8X + 38 = 98 \]
Now, subtract 38 from both sides:
\[ 8X = 98 - 38 \] \[ 8X = 60 \]
Finally, divide both sides by 8:
\[ X = \frac{60}{8} = 7.5 \]
Thus, the value of \( X \) is \( 7.5 \).
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