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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. 
November 21st, 2014, 08:44 AM  #3  
Senior Member Joined: Apr 2014 From: Europa Posts: 584 Thanks: 177  Quote:
would perhaps be clearer. So, you do that !  
November 21st, 2014, 09:36 AM  #4  
Member Joined: Sep 2014 From: Sweden Posts: 94 Thanks: 0  Quote:
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  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Hello, DecoratorFawn82! Quote:
Look at the "floor" of the cube. We have an $x\text{by}x$ square. Code: x *      *  *   *   *  x  *   *   * *      * Look at the right triangle with the space diagonal. Code: *  *  * 30 x  *  *  * *         * x√2 Solve for $x.$  
November 21st, 2014, 01:42 PM  #6  
Member Joined: Sep 2014 From: Sweden Posts: 94 Thanks: 0  Quote:
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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