question_answer

A 34 m long ladder reached a window 16 m from the ground on placing it against a wall. Find the distance of the foot of the ladder from the wall.

A)  \[40\text{ }m\]                       

B)  \[30\text{ }m\]           

C)  \[50\,m\]        

D)         \[10\,m\]         

Correct Answer: B

Solution :

Let AB = length of ladder, AC = height of window                           . In \[\Delta \,ABC,\]             \[{{(AB)}^{2}}={{(AC)}^{2}}+{{(BC)}^{2}}\]             \[\Rightarrow \] \[{{(34)}^{2}}={{(16)}^{2}}+B{{C}^{2}}\]             or  \[B{{C}^{2}}={{(34)}^{2}}-{{(16)}^{2}}\]             \[\Rightarrow \]  \[B{{C}^{2}}=1156-256=900\]             \[\therefore \]    \[BC=\sqrt{900}=30\,m\]