Question

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

Answer 1

Let AB be the width of the street and C be the foot of the ladder. Let D and E bethe windows at heights of 9 m and 12 m respectively from the ground. Then, CD and EF are the two positions of the ladder.

Clearly,$AD=9cm,BE=12cm,CD=CE=15m.$

In $△ACD$

By pythagoras theoram, we have

${CD}^2={AC}^2+{AD}^2$

$\Rightarrow$ ${15}^2={AC}^2+9^2$

$\Rightarrow$ ${AC}^2=225-81=144$

$\Rightarrow$ $AC=12m$

In $△BCE$,

By pythagoras theoram, we have

${CE}^2={BC}^2+{BE}^2$

$\Rightarrow$ ${15}^2={BC}^2+{12}^2$

$\Rightarrow$ ${BC}^2=225-144=81$

$\Rightarrow$ $BC=9m$

Hence, width of the street$=AB=AC+CB=(12+9)m=21m.$