# A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall

**Solution:**

This question is based on the concept of the right-angled triangle.

As it is clear from the figure that the ladder is kept slanted on the wall.

Hence, consider the length of the ladder as hypotenuse that is AB =15m and as it is kept slanted on the wall so, we consider the wall as perpendicular thst is AC = 12 m.

Now, you must find out the distance of the foot of the ladder from the wall that is BC = a.

Now by applying the Pythagoras theorem in triangle ABC, we can find out BC.

For better visual understanding draw a right-angled triangle consider ladder as hypotenuse, wall as perpendicular, and distance between the foot of the ladder and wall as the base.

Given, Length of ladder AB = 15 m Length of wall AC = 12 m

To find (BC) = distance of the foot of the ladder from the wall.

According to Pythagoras theorem,

(Hypotenuse)^{2} = (Perpendicular)^{2} + (Base)^{2 }

(AB)^{2 }= (AC)^{2 }+ (BC)^{2}

(15)^{2} = (12)^{2 }+ (a)^{2}

225 = 144 + (a)^{2}

225 - 144 = (a)^{2}

81 = a^{2}

a = 9 m

Therefore, the distance of the foot of the ladder from the wall is 9 m.

Useful Tip:

Whenever you encounter a problem of this kind, it is better to understand it visually.

**Video Solution:**

## A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall

### NCERT Solutions for Class 7 Maths - Chapter 6 Exercise 6.5 Question 3

A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall

The distance of the foot of the ladder from the wall is 9 m