1. **Problem statement:** We have a triangle with a perpendicular height of 12 units. The base is divided into two segments: one segment is $x$ and the other is 16. We want to find the value of $x$. 2. **Understanding the problem:** The height is perpendicular to the base, creating two right triangles inside the original triangle. The height splits the base into two parts: $x$ and 16. 3. **Using the Pythagorean theorem:** If the height is perpendicular, and the triangle sides form right angles, we can use the Pythagorean theorem to relate the sides. 4. **Set up the equation:** Suppose the hypotenuse of the right triangle adjacent to segment $x$ is 7 (from the problem title "7)" which likely indicates the hypotenuse length). Then, by the Pythagorean theorem: $$7^2 = 12^2 + x^2$$ 5. **Calculate:** $$49 = 144 + x^2$$ 6. **Solve for $x^2$:** $$x^2 = 49 - 144 = -95$$ 7. **Interpretation:** Since $x^2$ is negative, this is impossible for a real number $x$. This suggests either the hypotenuse is not 7 or more information is needed. **Alternative approach:** If the problem is to find the length $x$ given the height 12 and the other segment 16, and the triangle is right angled at the height, then the total base is $x + 16$. If the triangle is right angled, and the height is 12, then the area is: $$\text{Area} = \frac{1}{2} \times (x + 16) \times 12$$ But without more information, we cannot find $x$. **Conclusion:** The problem as stated lacks sufficient information to solve for $x$. Please provide the length of the hypotenuse or other side lengths. **Since the user asked for the answer and how to solve it, and the problem is incomplete, we cannot solve it.**