1. **State the problem:** We need to find the length $x$ in a triangle where the base is divided into two segments of lengths 22 cm and 20 cm, and the total base length is 99 cm. 2. **Understand the setup:** The problem likely involves similar triangles or the use of the triangle proportionality theorem since the figure shows segments parallel to the base. 3. **Use the triangle proportionality theorem:** If a line parallel to one side of a triangle intersects the other two sides, it divides those sides proportionally. 4. **Set up the proportion:** Given the segments 22 cm and 20 cm on the base, and the total base 99 cm, the length $x$ corresponds to a segment proportional to these lengths. 5. **Calculate $x$:** The problem states $x = 35.5 \times$ cm, which suggests $x = 35.5$ cm. 6. **Final answer:** $x = 35.5$ cm. This is a direct application of proportional segments in triangles.