A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 8 feet less than the length of the ladder. find the length of the ladder if the distance from the bottom of the ladder to the building is 16 feet.

This is the concept of application of Pythagorean theorem and algebra;

Suppose the the length of the ladder is x ft, the distance from the ground to the top of the ladder will be (x-8) ft, the distance from the bottom of the ladder to the building is 16ft, thus to find the length of the ladder we proceed as follows;

c^2=a^2+b^2

x^2 = (x-8) ^2+16^2

x^2=x^2-16x+64+256

collecting the like terms we get:

x^2-x^2+16x=320

16x=320

solving for x we get:

x=320/16

x=20 ft

the answer is x=20 ft