What is the length of the ladder if a ladder of length L is carried horizontally around a corner from a hall 3 feet wide into a hall 4 feet wide?
Consider a line segment running from
The minimum length of this line segment will be the maximum length of ladder that can be maneuvered around this corner.
[watch for the
By similar triangles we can see that
By the Pythagorean Theorem, we can express the square of the length of the line segment as a function of
Normally we would take the derivative of L(s) to find the minimum but in this case it is easier to take the derivative of
(Note that if
Taking the first derivative of
allows us to solve for
Plugging this value back into the equation for
the maximum ladder length