Question

A ladder of length 15 m reaches a window which is 9m above the ground on one side of
a street and at the same point it reaches a window 12 m high on a wall on opposite side.
Find the width of the street AB.

Answer 1

Step-by-step explanation:

ladder ht. same in both case = 15 m

in Δ APC by Pythagoras theorem

 CA² + AP² = CP² ⇒ CA² = 225 - 144 = 81 ⇒ CA = 9 m

similarly in ΔBPD

DB² + BP² = DP² ⇒  BP² = 225-81 = 144 ⇒ BP = 12m

width of street AB = AP+BP = 12+9= 21m

Answer 2

ANSWER

Length of ladder=AC=15m

Height of window from ground in first case AB=9m

ABC is right angled triangle

$\implies {AC}^{2} = {AB}^{2} + {BC}^{2}$

BC=12m

In second case

Let CE be length of ladder=15m

Height of window from ground=DE=12m

Triangle CDE is a right angled triangle

$\implies {CE}^{2}={DE}^{2}+{CD}^{2}$

CD=9m

Width of street=BC+CD=9+12=21m