Question

A 25-foot ladder is placed against a building. The bottom of the ladder is 7 feet from the building. If the top of the ladder slips down 4 feet, how mant feet will the bottom slide out?

Answer 1

As per the statement:

A 25-foot ladder is placed against a building. The bottom of the ladder is 7 feet from the building.

⇒Length of the ladder against a building = 25 foot

and Length of the bottom of the ladder from the building= 7 feet.

You had Before the slip.

Let x be the height of the building where ladder hits the building

By Pythagoras theorem:

`\text{Hypotenuse side}^2=\text{Perpendicular}^2+\text{Base}^2`

Here, Perpendicular side = Height of the building = x , Base = Length of the bottom of the ladder from the building = 7 foot and Hypotenuse side = 25 foot

Substitute the value to solve for x;

`25^2=x^2+7^2`

`625=x^2+49`

or

`x^2 = 625-49 = 576`

`x = √(576) = 24` foot.

⇒Height of the building = 24 foot

Now, if the ladder slips down 4 feet.

You had after slip

⇒Now, the height of the building becomes = 24-4 = 20 foot.

Let y be the distance from the building wall

then by Pythagoras theorem;

`y^2+20^2 = 25^2`

`y^2+400 =625`

`y^2 = 625-400 = 225`

`y=√(225) = 15` foot.

We have to find how many feet will the bottom slide out.

Since, Originally the distance of the bottom from the building = 7 foot

And now, the distance is = 15 foot.

The bottom slide out will be = 15 - 7 =8 foot

Therefore, 8 feet will the bottom slide out