1. **State the problem:** Identify the method used to solve for the top base length $x$ of a trapezoid given the bottom base and the lengths of the legs. 2. **Explanation:** The method involves using the Pythagorean theorem on the right triangles formed by dropping perpendiculars from the top base to the bottom base. 3. **Key idea:** By expressing the horizontal segments adjacent to the top base in terms of the height $h$ and the legs, and knowing the total bottom base length, we set up an equation involving square roots. 4. **Solving:** The problem reduces to solving for $h$ and then $x$ using algebraic manipulation and numerical approximation. 5. **Summary:** This approach is a combination of geometric decomposition and the Pythagorean theorem, often called the method of using right triangles within trapezoids to find unknown lengths. **Final answer:** The method used is the application of the Pythagorean theorem to right triangles formed inside the trapezoid, combined with algebraic and numerical solving techniques.