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### 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/
```
Associated Topics:
High School Geometry
High School Polyhedra
High School Triangles and Other Polygons
Middle School Geometry
Middle School Polyhedra
Middle School Triangles and Other Polygons

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