1. **State the problem:** Find the perimeter of triangle GIH with vertices at $G(-7,-8)$, $I(-3,-1)$, and $H(-1,-8)$. 2. **Formula:** The perimeter is the sum of the lengths of all sides. Use the distance formula between two points $A(x_1,y_1)$ and $B(x_2,y_2)$: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Calculate length GI:** $$GI = \sqrt{(-3 - (-7))^2 + (-1 - (-8))^2} = \sqrt{(4)^2 + (7)^2} = \sqrt{16 + 49} = \sqrt{65}$$ 4. **Calculate length IH:** $$IH = \sqrt{(-1 - (-3))^2 + (-8 - (-1))^2} = \sqrt{(2)^2 + (-7)^2} = \sqrt{4 + 49} = \sqrt{53}$$ 5. **Calculate length GH:** $$GH = \sqrt{(-1 - (-7))^2 + (-8 - (-8))^2} = \sqrt{(6)^2 + (0)^2} = \sqrt{36} = 6$$ 6. **Sum the lengths for perimeter:** $$P = GI + IH + GH = \sqrt{65} + \sqrt{53} + 6$$ 7. **Approximate values:** $$\sqrt{65} \approx 8.06, \quad \sqrt{53} \approx 7.28$$ $$P \approx 8.06 + 7.28 + 6 = 21.34$$ **Final answer:** The perimeter of triangle GIH is approximately $21.34$ units.