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How long is the diagnosal through the center of a particular

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How long is the diagnosal through the center of a particular [#permalink] New post 14 Sep 2003, 17:25
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How long is the diagnosal through the center of a particular cube?

1. A diagnosal across one face is 4.24 centimeters.
2.The surface area of the cube is 54 centimeters.

Please explain.

thanks!!
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Re: DS-the diagonsal [#permalink] New post 14 Sep 2003, 18:06
[quote="mystery"]How long is the diagnosal through the center of a particular cube?

1. A diagnosal across one face is 4.24 centimeters.
2.The surface area of the cube is 54 centimeters.

Please explain.

thanks!![/quote]

I think the answer is D

1-Sufficient
We must know that the square root (SQR; don't know how to do the symbol with the keyboard) of 2 = 1.414...., so 3sqr2= 4.24
And we also know that a cube has a squared surface, hence, its diagonal is similar to that of 90-45-45 triangle, which has the form Xsqr2.
Now of course, we know that we are talking about a 3 cm-sided cube.
But since the question is related to the diagonal that goes through the center of the cube, using the Pythagorean theorem, we just find the hypotenuse of the right triangle with sides 3 and, 3sqr2

2- Sufficient

54=6*(side^2); side=3; and then the reasoning is the same used above.
Re: DS-the diagonsal   [#permalink] 14 Sep 2003, 18:06
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