Question

Walls of two buildings on either side of a street are parallel to each other.A ladder 5.8 m long is placed on the street such that it's top just reaches the window of a building at the height of 4 m. On turning the ladder over to the other side of the street,it's top touches the window of the other building at a height 4.2 m. find the width of the street.

Answer 1

Answer:

The distance between the two buildings is 8.2 meters

Step-by-step explanation:

For better understanding of the solution, see the attached figure of the problem :

The window of both the buildings will be perpendicular to the ground surface of the street. So, according to figure, m∠ABC = m∠DEC = 90°

Now, let distance between ladder and first building be x meters ⇒ BC = x distance between ladder and second building be y meters ⇒ EC = y

In ΔABC, Using Pythagoras theorem, we have :

AC² = AB² + BC²

5.8² = 4² + x²

⇒ x² = 17.64

⇒ x = 4.2

In ΔDEC, Using Pythagoras theorem, we have :

DC² = DE² + EC²

5.8² = 4.2² + y²

⇒ y² = 16

⇒ y = 4

Now, distance between the two buildings = BE = BC + EC

⇒ BE = x + y

⇒ BE = 4.2 + 4

⇒ BE = 8.2 meters

Hence, the distance between the two buildings is 8.2 meters