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?

how tall is the ceiling?

I don't know how to find the mid point of an ellipse....back to grade 8 math for me.

8 metres would be my best guess without having any formula to rely on.

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 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?

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?