1. **Problem statement:** We are given a square ABCD with sides labeled as follows: AB = 18, BC = 3(y - 1), CD = 9x, and AD = 2y + 4. We need to find the values of $x$ and $y$. 2. **Important property:** In a square, all sides are equal in length. Therefore, we can set all side expressions equal to each other: $$18 = 3(y - 1) = 9x = 2y + 4$$ 3. **Set up equations:** From the equality of sides, we get two equations: - From AB and BC: $$18 = 3(y - 1)$$ - From AB and CD: $$18 = 9x$$ - From AB and AD: $$18 = 2y + 4$$ 4. **Solve for $y$ from the first equation:** $$18 = 3(y - 1)$$ Divide both sides by 3: $$6 = y - 1$$ Add 1 to both sides: $$y = 7$$ 5. **Solve for $x$ from the second equation:** $$18 = 9x$$ Divide both sides by 9: $$x = 2$$ 6. **Check $y$ with the third equation:** $$18 = 2y + 4$$ Subtract 4 from both sides: $$14 = 2y$$ Divide both sides by 2: $$y = 7$$ This matches the previous value of $y$, confirming our solution. **Final answers:** $$x = 2$$ $$y = 7$$