1. **State the problem:** We know the area of a square varies directly with the square of its side length. Given the area of the original square is 64 cm², and the side of the new square is doubled, we need to find: - The length of the side of the original square - The length of the side and area of the new square 2. **Formula and explanation:** The area $A$ of a square with side length $s$ is given by: $$A = s^2$$ This means the area varies directly with the square of the side. 3. **Find the side length of the original square:** Given $A = 64$, solve for $s$: $$s = \sqrt{A} = \sqrt{64} = 8$$ So, the side length of the original square is 8 cm. 4. **Find the side length of the new square:** The new side length is doubled: $$s_{new} = 2 \times 8 = 16$$ 5. **Find the area of the new square:** Using the formula: $$A_{new} = s_{new}^2 = 16^2 = 256$$ **Final answers:** - Original side length: 8 cm - New side length: 16 cm - New area: 256 cm²