Question

Question 3
A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall.

Answer 1

The given figure illustrates the situation mentioned in the question.
Let AC be the ladder and AB be the window.
Given: AC = 15 m, AB = 12 m, CB =a m
In right angled triangle ACB,
$(Hypotenuse{)}^2=(Base{)}^2+(Perpendicular{)}^2$
[By Pythagoras theorem]

$\Rightarrow (AC{)}^2=(CB{)}^2+(AB{)}^2\Rightarrow (15{)}^2=(a{)}^2+(12{)}^2\Rightarrow 225=a^2+144\Rightarrow a^2=225-144=81\Rightarrow a=\sqrt{81}=9m$
Thus, the distance of the foot of the ladder from the wall is 9 m.