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 November 21st, 2014, 06:16 AM #1 Member   Joined: Sep 2014 From: Sweden Posts: 94 Thanks: 0 Spacediagonal 30 cm in a cube? Calculate the cubes side lengths? Hi! I have this question about an exercise in my Swedish math book. It told me to calculate the cube's side lengths. But the only thing I know is the spacediagonal. Or whatever it's called in English. I think that it has something to do with Pythagoras theorem. First I thought that it was that I could calculate the cube sides length using: x^2 + x^2 = 30^2 But then I realized that the sides of the triangle isn't equal. So then I thought: a^2 + b^2 = 30^2 And after that I got stuck.  We can say that d = 30 in this image. Do you get it? I really appreciate help! Last edited by skipjack; November 21st, 2014 at 06:18 PM. November 21st, 2014, 08:22 AM #2 Banned Camp   Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191 If a is the length of the edge of the cube, then $\displaystyle \ a\sqrt{3} \$ is the length of the space diagonal of that cube. Source: Space diagonal - Wikipedia, the free encyclopedia Set $\displaystyle \ a\sqrt{3} \ = \ 30, \$ and solve for a. Thanks from DecoratorFawn82 November 21st, 2014, 08:44 AM   #3
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Quote:
 Originally Posted by DecoratorFawn82 Hi! I have this question about a exercise in my Swedish math book. It told me to calculate the cubes side lengths. But the only thing I know is the spacediagonal. Or whatever it's called in English.
In Swedish, the text of this problem

would perhaps be clearer.

So, you do that ! November 21st, 2014, 09:36 AM   #4
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 Originally Posted by Math Message Board tutor If a is the length of the edge of the cube, then $\displaystyle \ a\sqrt{3} \$ is the length of the space diagonal of that cube. Source: Space diagonal - Wikipedia, the free encyclopedia Set $\displaystyle \ a\sqrt{3} \ = \ 30, \$ and solve for a.
a sqrt(3) = 30
a = 30/(sqrt(3))
a = 17

Thanks! Your answer seem to be correct according to my facit in my math book . But could you please explain more in detail what exactly you are doing?

Where do you get sqrt(3) from? The volume of a cube x^3? Or that it is a triangle and it has 3 sides? And why would you take the square root of it?

I understand that a is the sides of the cube that we are going to calculate. But I do not really understand the sqrt(3).

Could you please explain? EDIT:

I saw that you wrote that it is the length of the space diagonal. But could you please explain more in detail?

Last edited by skipjack; November 21st, 2014 at 06:22 PM. November 21st, 2014, 12:11 PM   #5
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Hello, DecoratorFawn82!

Quote:
 The length of the space diagonal is 30. Find the length of the side of the cube. Look at the "floor" of the cube.

We have an $x\text{-by-}x$ square.

Code:
             x
* - - - - - *
| *          |
|   *        |
|     *      | x
|       *    |
|         *  |
|           *|
* - - - - - *
Its diagonal is $x\sqrt{2}.$

Look at the right triangle with the space diagonal.
Code:
      *
|  *
|     *   30
x |        *
|           *
|              *
* - - - - - - - - *
x√2
We have: $\:x^2 + (x\sqrt{2})^2 \:=\:30^2$

Solve for $x.$ November 21st, 2014, 01:42 PM   #6
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Quote:
 Originally Posted by soroban Hello, DecoratorFawn82! Look at the "floor" of the cube. We have an $x\text{-by-}x$ square. Code:  x * - - - - - * | * | | * | | * | x | * | | * | | *| * - - - - - * Its diagonal is $x\sqrt{2}.$ Look at the right triangle with the space diagonal. Code:  * | * | * 30 x | * | * | * * - - - - - - - - * x√2 We have: $\:x^2 + (x\sqrt{2})^2 \:=\:30^2$ Solve for $x.$
Is a diagonal of a cube always x*sqrt(2)?

So if x where 4 then it would be:

4*sqrt(2)?

Or where do you get sqrt(2) from?

Last edited by greg1313; November 21st, 2014 at 02:09 PM. November 21st, 2014, 06:27 PM #7 Global Moderator   Joined: Dec 2006 Posts: 20,835 Thanks: 2162 By Pythagoras, diagonal² = x² + x² = 2x², so diagonal = √2x. Tags calculate, cube, cubes, lengths, side, spacediagonal ,

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