question_answer

A ladder \[\text{25}\,\text{m}\] long just reaches the top of a building \[\text{24}\,\text{m}\]high from the ground. What is the distance of the foot of ladder from the base of the building?                          (CBSE 2020)

A) 5 m

B) 6 m

C) 7 m

D) 8 m

Correct Answer: C

Solution :

[c] Let AB be the ladder and CA be the building in which C is the base of the building.

Also,     \[AB=25\,m\]

and       \[CA=24\,cm\]

Now, in right \[\Delta ACB,\]

\[A{{B}^{2}}=B{{C}^{2}}+A{{C}^{2}}\]

(By Pythagoras theorem)

\[\Rightarrow \,\,\,\,\,\,B{{C}^{2}}=A{{B}^{2}}-A{{C}^{2}}\]

\[={{(25)}^{2}}-{{(24)}^{2}}\]

\[=(25-24)\,(25+24)=49\]

\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,BC=7\,m\]

So, the distance of the foot of the ladder from the base of the building is\[7\,m\].