Let AC be the position of a window from the ground and BC be the ladder, then the height of the window, AC = 12 m and length of the ladder, BC = 13m
Let AB = x m be the distance of the foot of the ladder from the base of the wall.
In ∆CAB, using Pythagoras Theorem,
(Perpendicular)2 + (Base)2 = (Hypotenuse)2
⇒ (AC)2 + (AB)2 = (BC)2
⇒ (12)2 + (AB)2 = (13)2
⇒ (AB)2 = (13)2 – (12)2
⇒ (AB)2 = (13 – 12)(13+12)
[∵ (a2 – b2)=(a + b)(a – b)]
⇒ (AB)2 = (1)(25)
⇒ (AB)2 = 25
⇒ AB = ±5
⇒ AB = 5 [taking positive square root]
Hence, the distance of the foot of the ladder from base of the wall is 5m