A5-foot ladder is leaning against a 4-foot wall. how far must the bottom of the ladder be from the base of the wall so that the top of the ladder rests on the top of the wall.

This is a classic example of a right angled triangle where the ladder is the hypotenuse and the wall and the base of the wall are the other 2 sides of the triangle.
  
Since it is a right angled triangle, Pythagorean theorem will be applied to it. 

So, we use the formula - 
hypotenuse^2 = side1^2 + side2^2

Here, hypotenuse (ladder) = 5 feet, side1 (wall) = 4 feet, side2 (base of the wall) = unknown.

So, we have, 5^2 = 4 ^2 + side2^2
==> side2^2 = 5^2 - 4^2 
==> side2^2 = 25 - 16
==> side2^2 = 9
==> side2 = square root (9)
==> side2 = 3

So, the final answer is --> the bottom of the ladder is 3 foot away from the base of the wall.

A right angled triangle is formed here.
By Pythagoras theorem,
H² = B² + L²
where L is the altitude (wall), B is the base (ground) and H is the hypotenuse (ladder).
⇒ 5² = B² + 4²
⇒ 25 = B² + 16
⇒ B² = 25 - 16 = 9
⇒ B = 3
The bottom of the ladder must be 3 feet away from the base of the wall.

You have to put the answer options on here in order for us to know which statement to tell you is correct.