HW The second side of a triangular deck is 4 feet longer than the shortest side, and the third side is 4 feet shorter than twice the length of the shortest side. If the perimeter of the dock is 52 foet, what ar \( 8.33 \%, 1 \) of 12 points the three sides? The shortest side of the deck is \( \square \) feet. (Simplify your answer.)

Let the length of the shortest side of the triangular deck be \( x \) feet. According to the problem: - The second side is \( x + 4 \) feet. - The third side is \( 2x - 4 \) feet. The perimeter of the triangle is given as 52 feet. Therefore, we can set up the equation: \[ x + (x + 4) + (2x - 4) = 52 \] Now, simplify the equation: \[ x + x + 4 + 2x - 4 = 52 \] Combine like terms: \[ 4x = 52 \] Now, solve for \( x \): \[ x = \frac{52}{4} = 13 \] Now that we have the shortest side, we can find the lengths of the other two sides: 1. The second side: \[ x + 4 = 13 + 4 = 17 \text{ feet} \] 2. The third side: \[ 2x - 4 = 2(13) - 4 = 26 - 4 = 22 \text{ feet} \] Thus, the lengths of the three sides of the triangular deck are: - Shortest side: \( 13 \) feet - Second side: \( 17 \) feet - Third side: \( 22 \) feet In conclusion, the shortest side of the deck is \( \boxed{13} \) feet.