Question

A ladder 26 m long reaches a window 24 m above the ground. Find the distance of the foot of the ladder from the base of the wall.

Answer 1

Let AC be the position of a window from the ground and BC be the ladder, then the height of the window, AC = 24 m and length of the ladder, BC = 26 m

Let AB = x m be the distance of the foot of the ladder from the base of the wall.

In ∆CAB, using Pythagoras Theorm,

(Perpendicular)² + (Base)² = (Hypotenuse)²

⇒ (AC)² + (AB)² = (BC)²

⇒ (24)² + (AB)² = (26)²

⇒ (AB)² = (26)² – (24)²

⇒ (AB)² = (26 – 24)(26+24)

[∵ (a² – b²)=(a+b)(a – b)]

⇒ (AB)² = (2)(50)

⇒ (AB)² = 100

⇒ AB = ±10

⇒ AB = 10 [taking positive square root]

Hence, the distance of the foot of the ladder from base of the wall is 10 m.