Question

# A ladder of $3.9m$ length is laid against a wall. The distance between the foot of the wall and the ladder is $1.5m$. Find the height at which the ladder touches the wall.(A) $3.6m$ (B) $4.55m$ (C) $4.82m$ (D) $5.7m$

According to the question, the length of the ladder is $3.9m$.
Hypotenuse,$H = 3.9m$ and Base$B = 1.5m$.
$\Rightarrow {\left( H \right)^2} = {\left( B \right)^2} + {\left( P \right)^2}, \\ \Rightarrow {P^2} = {H^2} - {B^2}, \\ \Rightarrow {P^2} = {\left( {3.9} \right)^2} - {\left( {1.5} \right)^2}, \\ \Rightarrow P = \sqrt {15.21 - 2.25} , \\ \Rightarrow P = \sqrt {12.96} , \\ \Rightarrow P = 3.6m \\$
Thus, the ladder touches the wall $3.6m$ above the ground.