Question

A ladder 25 m long reaches a window which is 15 m above the ground on one side of the street. When it turned to the other side keeping its foot at the same point, it touches a wall at a height of 20 m from the ground. Find the width of the street.

Answer 1

Given:

Ladder length = 25 m, heights reached = 15 m and 20 m on opposite walls; foot of ladder stays at the same point.

Step-wise calculation:

1. Let the width of the street be w and the distance from the foot of the ladder to the first wall be x.

2. By Pythagoras for the side where the ladder reaches 15 m:

x² + 15² 

= 25²x² + 225

= 625x² = 400

⇒ x = 20 m

3. For the other side distance from foot to that wall = w – x where ladder reaches 20 m:

(w – x)² + 20²

= 25²(w – 20)² + 400

= 625(w – 20)²

= 225w – 20 

= 15   ...(Rejecting the negative root because width must exceed x)

w = 35 m

The width of the street is 35 m.