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题目给出：在△ABC中，AB = AC，点D是BC延长线上一点，DE ⊥ AB 于E，AE = CD，△FDC的面积为3，EF = 4，求CF的长度。

### 解题思路：
1. **已知条件**：
   - △ABC 是等腰三角形，AB = AC。
   - D 在BC的延长线上，DE ⊥ AB，AE = CD。
   - △FDC的面积是3，EF = 4，要求求出CF的长度。

2. **几何分析**：
   - 因为AE = CD，且有等腰三角形，说明△ABC中的对称性比较重要。
   - 利用△FDC的面积公式，以及三角形面积公式 \( S = \frac{1}{2} \times 底 \times 高 \) 来求解未知量。

3. **面积公式的应用**：
   - △FDC的面积是3，已知EF的长度为4。可以用面积公式表示出三角形的底和高的关系。
   
4. **联立方程求解CF**：
   - 根据三角形面积与已知条件，通过几何关系推导出CF的值。

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Here are 5 related questions that may help deepen your understanding:
1. How can you apply the formula for the area of a triangle in problems involving heights and bases?
2. Why is the right-angle relationship between DE and AB important in this problem?
3. How does knowing that AB = AC help simplify calculations?
4. What other geometric properties might apply when dealing with a point on the extension of a line?
5. How could symmetry in an isosceles triangle help solve similar problems?

**Tip**: Always check for symmetry in problems involving isosceles triangles—this can often simplify the solution.

在△ABC中，AB=AC，点D是BC延长线上一点，DE⊥AB于E，AE=CD，△FDC的面积为3，EF=4，求CF的长度。

Solve the geometry problem where AB=AC, D is on the extended line of BC, and DE is perpendicular to AB. Given that AE=CD, the area of △FDC is 3, and EF=4, calculate CF. This problem involves triangle properties, area calculation, and symmetry in isosceles triangles. Suitable for high school students.

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