Question

A ladder 25 m long just reaches the top of a building 24 m high from the ground. What is the distance of the foot of the ladder from the building?
(a) 7 m
(b) 14 m
(c) 21 m
(d) 24.5 m

Answer 1

(a) 7 m

Let the ladder BC reaches the building at C.
Let the height of building where the ladder reaches be AC.
According to the question:
BC = 25 m
AC = 24 m
In right-angled triangle CAB, we apply Pythagoras theorem to find the value of AB.
$$\begin{gathered} B{C}^2=A{C}^2+A{B}^2 \\ \Rightarrow A{B}^2=B{C}^2-A{C}^2={25}^2-{24}^2 \\ \Rightarrow A{B}^2=625-576=49 \\ \Rightarrow AB=\sqrt{49}=7\mathrm{m} \end{gathered}$$