A fence 6 feet tall runs parallel to a tall building at a distance of 7 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?

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, the fence, and the distance from the fence to the building form a right triangle.

Let's label the length of the ladder as "L", the height of the fence as "6 feet", and the distance from the fence to the building as "7 feet".

Using the Pythagorean theorem, we can write the equation as:

L^2 = 6^2 + 7^2

Simplifying, we get:

L^2 = 36 + 49
L^2 = 85

Taking the square root of both sides, we get:

L = √85

Therefore, the length of the shortest ladder that will reach from the ground over the fence to the wall of the building is approximately √85 feet.

Have you considered drawing a sketch?

let x be the distance from the fence to the ladder base, so x+7 is the distance to the building from the ladder base.

x/6=(x+7)/h where height at the building intercept.

dx/6=dx/h-7/h^2 dh -x/h^2 dh

dx/dh (1/6-1/h)=-1/h^2 (7-x)

but dx/dh=0 so

x must 7

so length can be figured from
length=2(sqrt (16+49))

check that, I did it quickly.