Question

The upper end of a ladder touches a $12$ meter high window on one side of a street. The ladder is rotated to opposite side of the street keeping its foot fixed and touches a $9$ meter high window. If length of the ladder is $15m$, then find the width of the road.

• A. $15m$
• B. $9m$
• C. $21m$
• D. $12m$

Answer 1

The correct option is C $21m$

Let ladder $=BC=CD=15meter$
$B$ and $D$ are windows on opposite sides of street.
Given, $DE=9$ meter
$AB=12meter$
In right angled $△BAC$,
$A{C}^2+A{B}^2=B{C}^2$
$A{C}^2+{12}^2={15}^2$
$AC+144=225$
$A{C}^2=225-144=81$
$AC=\sqrt{81}=9metres$
In $△CED$
Similarly, $CE=\sqrt{{15}^2-9^2}=\sqrt{225-81}=\sqrt{144}=12metres$
$\therefore$ Width of the road $AE=AC+CE=9+12=21metre$.