1. **Problem Statement:** We have a square and an equilateral triangle with the same perimeter. The side length of the square is $3x + 9$. The side length of the equilateral triangle is $7x - 1$. We need to find the value of $x$. 2. **Formula for Perimeter:** - Perimeter of a square = $4 \times$ side length. - Perimeter of an equilateral triangle = $3 \times$ side length. 3. **Set up the equation:** Since the perimeters are equal, $$4(3x + 9) = 3(7x - 1)$$ 4. **Simplify both sides:** $$12x + 36 = 21x - 3$$ 5. **Solve for $x$:** Bring all $x$ terms to one side and constants to the other: $$12x - 21x = -3 - 36$$ $$-9x = -39$$ Divide both sides by $-9$: $$x = \frac{-39}{-9} = \frac{39}{9} = \frac{13}{3} \approx 4.33$$ 6. **Check answer choices:** The value $4.33$ is closest to option (c) 4. 7. **Conclusion:** The value of $x$ that makes the perimeters equal is approximately $4$, so the answer is (c) 4.