question_answer

A ladder \[\text{1}0\,\text{m}\] long reaches a window \[8\,\text{m}\] above the ground. The distance of the foot of the ladder from the base of the wall is: (NCERT EXERCISE)

A) 2 m

B) 18 m

C) 6 m

D) None of these 

Correct Answer: C

Solution :

[c] Let PR be the Ladder and PQ be the wall in which Q is the base of the wall

Also, \[PR=10\,m\]and \[PQ=8\,m\]

In right \[\Delta PQR,\] \[P{{R}^{2}}=P{{Q}^{2}}+R{{Q}^{2}}\]

\[\Rightarrow \,\,\,\,\,\,\,\,{{(10)}^{2}}={{(8)}^{2}}+R{{Q}^{2}}\]

\[\Rightarrow \,\,\,\,\,\,\,\,R{{Q}^{2}}=100-64=36\Rightarrow RQ=6m\]