We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the ladder, the wall, and the ground form a right triangle, with the ladder being the hypotenuse. Let x be the distance from the base of the wall to the bottom of the ladder. Then we have:
x^2 + 4^2 = 6^2
Simplifying the equation:
x^2 + 16 = 36
Subtracting 16 from both sides:
x^2 = 20
Taking the square root of both sides:
x = sqrt(20)
Simplifying:
x = 2sqrt(5)
Therefore, the bottom of the ladder is approximately 4.5 feet from the base of the wall.