Pole in a Box

Date: 02/09/99 at 18:18:07
From: Anonymous
Subject: Pythagoras

A removal truck comes to pick up a pole of length 6.5m. The dimensions 
of the truck are 3m, 3.5m, and 4m. Will the pole fit in the truck?

Thank you.

Date: 02/09/99 at 18:38:11
From: Doctor Wilkinson
Subject: Re: Pythagoras

I think you're supposed to think of the part of the truck not counting 
the wheels and the cab where the driver sits and so on, like a big box, 
say 4m long, 3m wide, and 3.5 m high. (It doesn't really matter which 
dimension is which). To get a really long object into the truck, you 
want to angle it so that it goes from one corner on the floor to the 
opposite corner on the ceiling.

So the question is, how far is it from one corner on the floor to the
opposite corner on the ceiling? To figure this out, we use Pythgoras's 
Theorem twice.

First of all, we can figure out the length of the diagonal of the floor 
of the truck. It's 3 feet wide and 4 feet long, so it's 5 feet on the 
diagonal, using the well-known 3-4-5 right triangle (3 squared plus 
four squared = 5 squared).

Now you get another right triangle if you take the diagonal as one side 
and the height of the truck from one end of the diagonal to the ceiling 
as the other. So we have a right triangle with one side of 5 and one 
side of 3.5. We can find the hypotenuse by Pythagoras's Theorem: the 
square of the hypotenuse is 3.5 squared + 5 squared, which is 37.25. 
This is less than 6.5 squared, so the pole will not fit.

- Doctor Wilkinson, The Math Forum
  http://mathforum.org/dr.math/