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

Answer:

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

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 10m