2019 · Q86
A ladder is resting against a vertical wall and its bottom is 2.5 m away from the wall. If it slips 0.8 m down the wall, then its bottom will move away from the wall by 1.4 m. What is the length of the ladder?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A6.2 m
- B6.5 m
- C6.8 m
- D7.5 m
Explanation
Let the initial height of the top be h metres; the ladder length L satisfies L^2 = h^2 + 2.5^2. After slipping, the foot is 2.5 + 1.4 = 3.9 m from the wall and the top is at h - 0.8, so L^2 = (h-0.8)^2 + 3.9^2. Equating gives h^2 + 6.25 = h^2 - 1.6h + 15.85, so 1.6h = 9.6 and h = 6. Then L = sqrt(36 + 6.25) = sqrt(42.25) = 6.5 m, option (b).