Question

A ladder 15m long reaches a window which is 12m above the ground on the side

of the street. Keeping its foot at the same point, the ladder is turned to the other

side of the street to reach window 9m high. Find the width of the street.​

Answer 1

$\huge{ \pink{ \boxed{ \blue{ \underline{ \red{ \mathbb{AnSwEr \: ❣}}}}}}}</p><p>$

${ \blue{ \boxed{ \green{ \underline{ \pink{using \: pythagoras \: theorem}}}}}}$

In ∆ABC ,

$AC² = AB² + BC² \\ \\ BC = \sqrt{AC² - AB²} \\ \\ = \sqrt{ {15}^{2} - {12}^{2} } \\ \\ = \sqrt{225 - 144} \\ \\ = \sqrt{81} \\ \\ BC = 9m$

${ \red{ \boxed{ \pink{ \underline{ \green{again \: using \: Pythagoras \: theorem}}}}}}$

In ∆CDE ,

$CD = \sqrt{CE² - ED²} \\ \\ = \sqrt{ {15}^{2} - {9}^{2} } \\ \\ = \sqrt{225 - 81} \\ \\ = \sqrt{144} \\ \\ CD = 12m$

Width of the street = BC + CD

= (9+12)m

= 21m