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

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Intern
Joined: 07 May 2016
Posts: 25
The figure ABCDEFGH is a cube. AB = 10. What is the length of the line  [#permalink]

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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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Joined: 02 Aug 2009
Posts: 8308
The figure ABCDEFGH is a cube. AB = 10. What is the length of the line  [#permalink]

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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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