A fence 5 feet tall runs parallel to a tall building at a distance of 5 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?

Consider similar triangles:

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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 length 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 of a right triangle, with the fence and the distance from the building forming the other two sides.

Let's label the sides of the triangle as follows:
- The height of the fence: 5 feet
- The distance from the building: 5 feet
- The length of the ladder (hypotenuse): ?

Using the Pythagorean theorem, we can set up the equation:
(length of the ladder)^2 = (height of the fence)^2 + (distance from the building)^2

Substituting the given values, we get:
(length of the ladder)^2 = 5^2 + 5^2
(length of the ladder)^2 = 25 + 25
(length of the ladder)^2 = 50

Now, we can solve for the length of the ladder by taking the square root of both sides:
length of the ladder = √50
length of the ladder ≈ 7.07 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 7.07 feet.