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### Distance Between Opposite Corners of a Box

```Date: 05/09/2002 at 16:26:31
From: Shemla
Subject: Word problem

Dr. Math,

I am having a hard time solving this math problem. Can you please
help me?

A moth is sitting in the lower left front corner of a storage
shed.  The shed's interior wall dimensions are 8 ft. by 12 ft. by
9 ft.

What is the distance, in feet, of the shortest path that the moth
can fly to the upper right back corner of the shed?
```

```
Date: 05/10/2002 at 08:34:59
From: Doctor Ian
Subject: Re: Word problem

Hi Shemla,

Let's look at a cube, in which each side has length 1:

D
+--------+
/        /|
/        / |
+--------+  |
|        |  + C
|        | /
|        |/
+--------+
A        B

I can use the Pythagorean theorem to find the distance from A to
C:

AC^2 = AB^2 + BC^2

AC = sqrt(AB^2 + BC^2)

= sqrt(1^2 + 1^2)

= sqrt(2)

Now I can do the same thing to find the distance from A to D:

= sqrt( sqrt(2)^2 + 1^1)

= sqrt(2 + 1)

= sqrt(3)

Can you use the same idea to find the distance between opposite
corners of the shed?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Three-Dimensional Geometry
Elementary Triangles and Other Polygons
Middle School Higher-Dimensional Geometry
Middle School Triangles and Other Polygons

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