Square Diagonal 91590E

1. **State the problem:** We are given the diagonal of a square as $$9\sqrt{2}$$ meters. We need to find the length of one side and the area of the square. 2. **Formula used:** For a square with side length $$s$$, the diagonal $$d$$ is given by the Pythagorean theorem: $$d = s\sqrt{2}$$ 3. **Find the side length:** Given $$d = 9\sqrt{2}$$, substitute into the formula: $$9\sqrt{2} = s\sqrt{2}$$ 4. **Divide both sides by $$\sqrt{2}$$ to isolate $$s$$:** $$\frac{9\cancel{\sqrt{2}}}{\cancel{\sqrt{2}}} = \frac{s\cancel{\sqrt{2}}}{\cancel{\sqrt{2}}}$$ $$9 = s$$ So, the side length $$s = 9$$ meters. 5. **Find the area:** The area $$A$$ of a square is: $$A = s^2$$ Substitute $$s = 9$$: $$A = 9^2 = 81$$ **Final answers:** - Side length = $$9$$ meters - Area = $$81$$ square meters