# Longest ladder in a hallway

PBE6
Posers and Puzzles 23 Mar '07 17:43
1. PBE6
Bananarama
23 Mar '07 17:431 edit
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?
2. uzless
The So Fist
23 Mar '07 17:553 edits
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.
3. ChronicLeaky
Don't Fear Me
23 Mar '07 17:58
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?
What's a 3x5 metre square?
4. PBE6
Bananarama
23 Mar '07 18:04
Originally posted by ChronicLeaky
What's a 3x5 metre square?
Haha, oops! That should say "rectangle"...
5. 23 Mar '07 18:521 edit
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?
6. uzless
The So Fist
23 Mar '07 19:142 edits
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?
7. DeepThought
24 Mar '07 01:35
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?
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