In the road of our locality there is a ladder of 15m. length kept in such a way that it has touched Milli’s window at a height of 9m. above the ground. Now keeping the foot of the ladder at the same point of that road. The ladder is rotated in such a way that it touched our window situated on the other side of the road. If our window is 12m. above the ground, then let us determine the breadth of that road in our locality.

Given: Length of ladder, l = 15 m

Now, the situation can be shown in a diagram as:

As the wall is always perpendicular to the floor or road, so ΔAFD and ΔBFC are right angled triangle.

Here b_road represents breadth of road.

To find b_road first we need to find the lengths AF and FB.

In right ΔAFD,

h = 15 m

p = 12 m

b = AF

By applying Pythagoras theorem, we have,

h² = p² + b²

⇒ 15² = 12² + AF²

⇒ 225 = 144 + AF²

⇒ AF²= 225 – 144

⇒ AF² = 121

⇒ AF = √121

⇒ AF = 11 m …………………… (1)

In right ΔBFC,

h = 15 m

p = 9 m

b = FB

By applying Pythagoras theorem, we have,

h² = p² + b²

⇒ 15² = 9² + FB²

⇒ 225 = 81 + FB²

⇒ FB² = 225 – 81

⇒ FB² = 144

⇒ FB = √144

⇒ FB = 12 m …………………… (2)

Now,

b_road = AF + FB

Substituting from eqn. (1) and (2), we have,

b_road = 11 + 12 m

b_road = 13 m

Therefore, the breath of road is 13 m.