1. **Problem statement:** We have a right triangle GHD with a right angle at H. The hypotenuse GD is 18 units, side GH is 14 units, and we need to find the length HD. 2. **Identify the triangle sides:** Since GHD is a right triangle with right angle at H, by the Pythagorean theorem: $$GD^2 = GH^2 + HD^2$$ 3. **Apply the Pythagorean theorem:** Substitute the known values: $$18^2 = 14^2 + HD^2$$ 4. **Calculate squares:** $$324 = 196 + HD^2$$ 5. **Isolate $HD^2$:** $$HD^2 = 324 - 196 = 128$$ 6. **Find HD:** $$HD = \sqrt{128} = \sqrt{64 \times 2} = 8\sqrt{2} \approx 11.3$$ 7. **Answer:** The length HD rounded to the nearest tenth is **11.3** units.