A fence 4 feet tall runs parallel to a tall building at a distance of 2 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?

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To find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the ladder forms the hypotenuse, the fence forms one side, and the distance between the building and the fence forms the other side.

Let's denote the length of the ladder as L. According to the problem, the fence is 4 feet tall and the distance between the fence and the building is 2 feet.

Using the Pythagorean theorem, we can write the equation:

L^2 = 4^2 + 2^2

Simplifying:

L^2 = 16 + 4

L^2 = 20

To find the length of the ladder, we take the square root of both sides:

L = √20

L ≈ 4.47 feet

Therefore, the length of the shortest ladder that will reach from the ground over the fence to the wall of the building is approximately 4.47 feet.