Longest ladder in a hallway

This one may have been asked before, but it's relatively simple so let's give it a go:

A construction crew is trying to bring a ladder down a hallway that changes size at the corner. The initial hallway section is 3 metres wide, and the second hallway section is 5 metres wide (from the top view, the corner is a 3x5 metre rectangle). If the crew must carry the ladder horizontally under their arms, and the ladder is of negligible thickness, how long a ladder can the crew fit through the hallway?

Originally posted by PBE6
This one may have been asked before, but it's relatively simple so let's give it a go:

A construction crew is trying to bring a ladder down a hallway that changes size at the corner. The initial hallway section is 3 metres wide, and the second hallway section is 5 metres wide (from the top view, the corner is a 3x5 metre square). If the crew must carry the ...[text shortened]... the ladder is of negligible thickness, how long a ladder can the crew fit through the hallway?

Originally posted by PBE6
This one may have been asked before, but it's relatively simple so let's give it a go:

A construction crew is trying to bring a ladder down a hallway that changes size at the corner. The initial hallway section is 3 metres wide, and the second hallway section is 5 metres wide (from the top view, the corner is a 3x5 metre square). If the crew must carry the ...[text shortened]... the ladder is of negligible thickness, how long a ladder can the crew fit through the hallway?

Originally posted by ChronicLeaky
What's a 3x5 metre square?

Originally posted by PBE6
This one may have been asked before, but it's relatively simple so let's give it a go:

A construction crew is trying to bring a ladder down a hallway that changes size at the corner. The initial hallway section is 3 metres wide, and the second hallway section is 5 metres wide (from the top view, the corner is a 3x5 metre rectangle). If the crew must carry ...[text shortened]... the ladder is of negligible thickness, how long a ladder can the crew fit through the hallway?

Originally posted by davegage
I would say we need to find the minimum of the following function over the interval X in [0, Pi/2]:

f(X) = 3/SinX + 5/CosX

I get something like ~11.19 m. Does that sound about right?

Originally posted by davegage
I would say we need to find the minimum of the following function over the interval X in [0, Pi/2]:

f(X) = 3/SinX + 5/CosX

I get something like ~11.19 m. Does that sound about right?

Originally posted by DeepThought
I get the same answer.