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# A cube has sides measuring 6 inches. What is the greatest

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A cube has sides measuring 6 inches. What is the greatest  [#permalink]

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Updated on: 21 May 2013, 01:15
00:00

Difficulty:

55% (hard)

Question Stats:

33% (01:37) correct 67% (00:27) wrong based on 9 sessions

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A cube has sides measuring 6 inches. What is the greatest possible (straight line) distance, in inches, between any two points on the box?

I read the explanation and understand that the greatest possible distance is from one opposite corner to the other (diagonal). I also understand how to find the diagonal of a face of the cube using the ratios of a 45-45-90 triangle. The diagonal is 6 sqrt of 2. This is where I get stuck. How do I use the diagonal of a face to come up with the diagonal of the entire cube?

Thanks!

Originally posted by josemnz83 on 20 May 2013, 14:51.
Last edited by Bunuel on 21 May 2013, 01:15, edited 1 time in total.
Renamed the topic and edited the question.
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20 May 2013, 15:03
Look at the image.

You use Pythagora:$$6^2+(6\sqrt{2})^2$$
take the root
$$6\sqrt{3}$$

Let me know if it's clear
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Re: A cube has sides measuring 6 inches. What is the greatest  [#permalink]

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21 May 2013, 01:18
josemnz83 wrote:
A cube has sides measuring 6 inches. What is the greatest possible (straight line) distance, in inches, between any two points on the box?

I read the explanation and understand that the greatest possible distance is from one opposite corner to the other (diagonal). I also understand how to find the diagonal of a face of the cube using the ratios of a 45-45-90 triangle. The diagonal is 6 sqrt of 2. This is where I get stuck. How do I use the diagonal of a face to come up with the diagonal of the entire cube?

Thanks!

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Hope it helps.
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Re: A cube has sides measuring 6 inches. What is the greatest   [#permalink] 21 May 2013, 01:18
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