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A cube has 4 as a side’s length. If A and B are midpoints

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A cube has 4 as a side’s length. If A and B are midpoints

by Max@Math Revolution » Mon Mar 28, 2016 3:57 am
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A cube has 4 as a side's length. If A and B are midpoints of each side and C is a vertex of the cube, what is the length of AB?

A. 2√3
B. 3√6
C. √6
D. 3√2
E. 2√6


* A solution will be posted in two days.
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by shona04 » Mon Mar 28, 2016 5:00 am
IMO.E

Took quiet some time to calculate. Any easy approach?
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by regor60 » Mon Mar 28, 2016 8:42 am
shona04 wrote:IMO.E

Took quiet some time to calculate. Any easy approach?
Quick, less than a minute, if you recognize that AB is the square root of the sum of the squares of AC and BC.

BC is obviously 2. AC is itself the square root of the sum of the squares of the distances to the vertex between them, 2 and 4.
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by Max@Math Revolution » Tue Mar 29, 2016 11:14 pm
A cube has 4 as a side's length. If A and B are midpoints of each side and C is a vertex of the cube, what is the length of AB?

A. 2√3
B. 3√6
C. √6
D. 3√2
E. 2√6


According to Pythagoras' theorem, AC^2=2^2+4^2=20 is derived.
Suppose AB is x and x^2=2^2+AC^2=24 is derived.
Then, x=√24=2√6.
Thus, E is the answer.
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