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:

  AD^2 = AC^2 + CD^2

    AD = sqrt(AC^2 + CD^2)

       = 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/