Question

A ladder $15m$ long reaches a window which is a $9m$ above the ground on one side of the street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window $12m$ high. Find the width of the street.

• A. $21m$
• B. $22m$
• C. $23m$
• D. $25m$

Answer 1

The correct option is A $21m$

In $△ADC$,
$A{D}^2+A{C}^2=C{D}^2$
$9^2+A{C}^2={15}^2$
$A{C}^2=225-81$
$AC=12$ m
In $△BEC$,
$E{C}^2=B{C}^2+B{E}^2$
${15}^2={12}^2+B{C}^2$
$225-144=B{C}^2$
$BC=9$ m
Width of the road = $AC+BC$ = $12+9$ = 21 m