# 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?

##### 1 Answer

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.

Suppose that

[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

Multiplying by

allows us to solve for

Plugging this value back into the equation for

the maximum ladder length