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09 May 2009, 16:30
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Square ABCD is the base of the cube while square EFGH is the cube's top facet such that point E is above point A, point F is above point B etc. What is the distance between the midpoint of edge AB and the midpoint of edge EH if the area of square ABCD is 2?
* \(\frac{1}{\sqrt{2}}\)
* 1
* \(\sqrt{2}\)
* \(\sqrt{3}\)
* \(2\sqrt{3}\)
* \(\frac{1}{\sqrt{2}}\)
* 1
* \(\sqrt{2}\)
* \(\sqrt{3}\)
* \(2\sqrt{3}\)
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10 May 2009, 00:57
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icandy
Square ABCD is the base of the cube while square EFGH is the cube's top facet such that point E is above point A, point F is above point B etc. What is the distance between the midpoint of edge AB and the midpoint of edge EH if the area of square ABCD is 2?
* \(\frac{1}{\sqrt{2}}\)
* 1
* \(\sqrt{2}\)
* \(\sqrt{3}\)
* \(2\sqrt{3}\)
* \(\frac{1}{\sqrt{2}}\)
* 1
* \(\sqrt{2}\)
* \(\sqrt{3}\)
* \(2\sqrt{3}\)
mathmatical approach:
say midpoint of AB = X
mid point of AD =Y
mid point of EF= Z
distance between X AND y = sqrt ((1/sqrt(2) )^2 +(1/sqrt(2) )^2) =1
distance between Z ABD X = sqrt((1)^2 +(sqrt(2))^2) =sqrt(3)
15 Oct 2009, 09:20
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I'm going to say sqrt 3.
The distance between midpoint AB and midpoint AD is a pythagorum theorum.
Since Area of ABCD is 2 we know each side is sqrt 2.
Therefore midpoint AB = .5 \sqrt{2} and AD = .5 \sqrt{2}
Therefore distance between midpoints AB and AD is sqrt 2
Midpoint between EH and AD is also sqrt 2 (straight line) Add them together and we get 2
We now know that since it is being cut through the square the distance is less 2 but definately more than sqrt 2.
Only sqrt 3 give this answer.
The distance between midpoint AB and midpoint AD is a pythagorum theorum.
Since Area of ABCD is 2 we know each side is sqrt 2.
Therefore midpoint AB = .5 \sqrt{2} and AD = .5 \sqrt{2}
Therefore distance between midpoints AB and AD is sqrt 2
Midpoint between EH and AD is also sqrt 2 (straight line) Add them together and we get 2
We now know that since it is being cut through the square the distance is less 2 but definately more than sqrt 2.
Only sqrt 3 give this answer.
