A 25 foot ladder is propped against the side of a building. The bottom of the ladder is 7 feet from the base of the wall. If the top of the ladder slides down 4 feet, how far does the bottom slide out?

1 Answer
Oct 17, 2017

See a solution process below:

Explanation:

In this problem we have this situation:

enter image source here

We can find how far up the wall the ladder is using the Pythagorean Theorem.

#7^2 + b^2 = 25^2#

#49 + b^2 = 625#

#-color(red)(49) + 49 + b^2 = -color(red)(49) + 625#

#0 + b^2 = 576#

#b^2 = 576#

#sqrt(b^2) = sqrt(576)#

#b = 24#

We now know the ladder is 24 feet up the wall. If the top of the ladder slides down 4 feet it will be 20 feet up the wall and we will have this situation:

enter image source here

We can again use the Pythagorean Theorem to solve for #a# this time.

#a^2 + 20^2 = 25^2#

#a^2 + 400 = 625#

#a^2 + 400 - color(red)(400) = 625 - color(red)(400)#

#a^2 + 0 = 225#

#a^2 = 225#

#sqrt(a^2) = sqrt(225)#

#a = 15#

The ladder is now 15 feet away from the wall. It was originally 7 feet away from the wall.

Therefore the ladder slid 8 feet further away from the wall when it slid 4 feet down the wall.