2018 · Q75
The length of a line segment AB is 2 cm. It is divided into two parts at a point C such that AC² = AB × CB. What is the length of CB?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A3√5 cm
- B3 - √5 cm
- C5√3 cm
- D√5 - 1 cm
Explanation
Let AC = x, so CB = 2 − x. Then x² = 2(2 − x) gives x² + 2x − 4 = 0, i.e. x = √5 − 1 (positive root). Hence CB = 2 − x = 3 − √5 cm, option (B). This is the golden-section division.