Question

A $15m$ long ladder is placed against a wall to reach a window $12m$ high. Find the distance of the foot of the ladder from the wall.

Answer 1

In figure,

length of the ladder $\left(AB\right)=15m$

Altitude of the window $\left(BC\right)=12m$

Let, the distance of the foot of the ladder from the wall be $x$.

$\angle ADC={90}^{\circ }$

By Pythagoras theorem in $△ABC$
$A{B}^2=A{C}^2+B{C}^2$
$\Rightarrow {15}^2=x^2+{12}^2$

$\Rightarrow 225=x^2+144$

$\Rightarrow 225-144=x^2$

$\Rightarrow 81=x^2$

$\Rightarrow 9^2=x^2$

$\Rightarrow 9=x$
Hence, the distance of the foot of the ladder from the wall is $9m$.