A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 3 feet less than the length of the ladder.

Question

find the length of the ladder if the distance from the bottom of the ladder to the building is 9 feet.

Answer 1

We have a right triangle formed by the ladder, the building and the ground.

 

The base is 9ft, as given in the problem.  And the height is 3 feet less than the hypotenuse, lets call the hypotenuse x, and the height x-3...

 

Pythagoras tells us that 9^2+(x-3)^2 = x^2

 

Expand this out solve for x.

 

81+x^2-6x+9=x^2 

90-6x=0

x=15