1. **State the problem:** We have a square pyramid with a base side length of 12 units and a vertical height of 15 units. We need to find the length $s$, which is the slant height of one of the triangular faces. 2. **Understand the geometry:** The slant height $s$ is the height of the triangular face from the apex to the midpoint of a base edge. 3. **Find the distance from the center of the base to the midpoint of a base edge:** Since the base is a square with side length 12, the midpoint of a base edge is 6 units from the center (half of 12). 4. **Use the Pythagorean theorem:** The vertical height (15 units), the distance from the center to the midpoint of the base edge (6 units), and the slant height $s$ form a right triangle. 5. **Apply the formula:** $$s = \sqrt{15^2 + 6^2}$$ 6. **Calculate:** $$s = \sqrt{225 + 36} = \sqrt{261}$$ 7. **Find the decimal value:** $$s \approx 16.1554944214$$ 8. **Round to the nearest tenth:** $$s \approx 16.2$$ **Final answer:** The length of $s$ is approximately 16.2 units.