A ladder lies against a wall.the top of the ladder reaches 8feet above the ground. when the ladder slips 2meters away from the wall,the top of the ladder touches the foot of the wall.then length of the wall?

To find the length of the wall, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the ladder forms a right triangle with the wall and the ground. Let's assume the length of the ladder is 'L' and the distance of the ladder's foot from the wall is 'd'.

According to the given information:
The ladder reaches 8 feet above the ground, and when it slips 2 meters away from the wall, it touches the foot of the wall. This forms a right triangle.

So, we have two sides of the triangle: the height of the wall (8 feet) and the distance of the ladder's foot from the wall (2 meters). We need to find the length of the wall.

Using the Pythagorean theorem, we have:
L^2 = 8^2 + d^2

When the ladder slips 2 meters away from the wall, it touches the foot of the wall, forming a right angle with the ground. So, the length of the ladder becomes the hypotenuse of the right triangle formed by the wall, ground, and ladder.

Now, let's use the second set of information provided:

When the ladder slips 2 meters away from the wall, the top of the ladder touches the foot of the wall. This means the height of the ladder (8 feet) also becomes the length of the wall. So, we can write:

L = 8

Plugging this value into the first equation, we have:

8^2 = 8^2 + d^2

64 = 64 + d^2

d^2 = 64 - 64

d^2 = 0

Therefore, the distance of the ladder's foot from the wall is 0. This means the ladder's foot is against the wall.

Hence, the length of the wall is equal to the length of the ladder, which is 8 feet.