A fence 8 ft high (w) runs parallel to a tall building and is 24 ft (d) from it. Find the length (L) of the shortest ladder that will reach from the ground across the top of the fence to the wall of the building.

25.3 ft

Explanation:

The illustration of the problem is shown the attached image.

The length of the ladder can be calculated using the Pythagoras theorem:

The hypotenuse is the length of the ladder.

........1

Triangle ABC is similar to triangle AEF, hence:

BC = .................2

Substitute 2 into 1

= +

Let AE = x

=

    =

Minimize L with respect to x.

2 =

       =

this is poiselle's equation from fluid mechanic in physics. mech eng