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The figure ABCDEFGH is a cube. AB = 10. What is the length of the line

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The figure ABCDEFGH is a cube. AB = 10. What is the length of the line  [#permalink]

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New post 11 May 2016, 20:19
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The figure ABCDEFGH is a cube. AB = 10. What is the length of the line segment AF?
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The figure ABCDEFGH is a cube. AB = 10. What is the length of the line  [#permalink]

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New post 11 May 2016, 21:21
HungNguyen wrote:
The figure ABCDEFGH is a cube. AB = 10. What is the length of the line segment AF?


Hi,
the formula for same is = SIDE *\(\sqrt{3}\) =\(10\sqrt{3}\)..

Just for info.. - how (Side *\(\sqrt{3}\)) comes?

Take any face of the cube, say bottom face - AHDE,
its diagonal, AE= \(\sqrt{SUM- of- square -of -two- sides}\) = \(\sqrt{AD^2+DE^2} = \sqrt{10^2+10^2} = 2\sqrt{10}\)..

Now take triangle AEF, AF is the hyp and AE and EF are two sides...
so AF = \(\sqrt{(2*\sqrt{10})^2+10^2} = \sqrt{10^2(2+1)} = 10\sqrt{3}\)
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The figure ABCDEFGH is a cube. AB = 10. What is the length of the line   [#permalink] 11 May 2016, 21:21
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The figure ABCDEFGH is a cube. AB = 10. What is the length of the line

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