Question

A 25-foot25−foot ladder is placed against a building. The bottom of the ladder is 77 feet from the building. If the top of the ladder slips down 44 feet, how many feet will the bottom slip?

Answer 1

The bottom of ladder slip to 8 feet.

Explanation:

Here is the given length or distance in question after avoiding typo error,

Length of ladder (h) = 25 ft

Ladder distance from building (
`b_1`) = 7 ft

The top of ladder slip down to 4 ft

Let p be the height of building.

Now, using Pythagoras formula to solve it

`p^(2) = h^(2) - b^(2)`

Next putting the value in the formula

`p^(2) = 25^(2) - 7^(2) = 625 - 49`

⇒
`p= √(576) = 24`

∴ Height of building (p) =
`24 \ ft`

As ladder slip down to 4 ft

∴ Now, the height from top of ladder to bottom of building =
`p-4 = 24 - 4= 20\ ft`

Let
`b_2` be the base of ladder from building

Again using Pythagoras formula,

`b^(2) = 25^(2) - 20^(2) = 625 - 400`

∴
`b= √(225) = 15 ft`

`b_2 = 15\ ft`

Now, we have the distance of base of ladder from building after slip is 15 ft.

Next step is to find length of bottom of ladder further slip.

⇒ Bottom of ladder slip =
`b_2- b_1`

∴ Bottom of ladder slip =
`15 - 7= 8 \ ft`