Question

A ladder 15m long reaches a window which is 9m 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 12m high. Find the width of the street.

Answer 1

let O be the foot of the ladder. Let AO be the position of the ladder when it touches the window at A which is 9m high and CO be the position of the ladder when it touches the window at C which is 12m high.
Using Pythagoras theorem,
In ΔAOB,
BO² = AO² - AB²
BO² = (15m)² - (9m)²
BO² = 225m² - 81m²
BO2 = 144m²
BO2 = (12m)²
BO2 = 12m
Using Pythagoras theorem in ΔCOB,
DO² = CO² - CD²
DO² = (15m)² - (12m)²
DO² = 225m² - 144m²
DO² = 81m²
DO = 9m
Width of the street 
= DO + BO
= 9m + 12m
= 21m.