1. **State the problem:** We are given three points $F(2,9)$, $G(-7,0)$, and $H(-1,1)$ that form a triangle. We need to find the perimeter of this triangle. 2. **Formula used:** The perimeter of a triangle is the sum of the lengths of its sides. The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Calculate each side length:** - Length $FG$: $$FG = \sqrt{(-7 - 2)^2 + (0 - 9)^2} = \sqrt{(-9)^2 + (-9)^2} = \sqrt{81 + 81} = \sqrt{162}$$ - Length $GH$: $$GH = \sqrt{(-1 + 7)^2 + (1 - 0)^2} = \sqrt{6^2 + 1^2} = \sqrt{36 + 1} = \sqrt{37}$$ - Length $HF$: $$HF = \sqrt{(2 + 1)^2 + (9 - 1)^2} = \sqrt{3^2 + 8^2} = \sqrt{9 + 64} = \sqrt{73}$$ 4. **Simplify and approximate:** $$FG \approx \sqrt{162} = \sqrt{81 \times 2} = 9\sqrt{2} \approx 12.7$$ $$GH \approx \sqrt{37} \approx 6.1$$ $$HF \approx \sqrt{73} \approx 8.5$$ 5. **Find the perimeter:** $$\text{Perimeter} = FG + GH + HF \approx 12.7 + 6.1 + 8.5 = 27.3$$ **Final answer:** The perimeter of the triangle is approximately $27.3$ units.