Square ABCD is the base of the cube while square EFGH is the

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Square ABCD is the base of the cube while square EFGH is the [#permalink]

27 Nov 2007, 00:24

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Square ABCD is the base of the cube while square EFGH is the cube's top face 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?

1/sqrt2
1
sqrt2
sqrt3
2sqrt3

Please explain your answer.

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Re: PS Cube [#permalink]

27 Nov 2007, 00:33

bmwhype2 wrote:

distance from mid point of AB to AD = sqrt [(1/sqrt2)^2+(1/sqrt2)^2] = 1

the distance between the midpoint of edge AB and the midpoint of edge EH = sqrt [1^2+(sqrt2)^2] = sqrt3.

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Re: PS Cube [#permalink]

27 Nov 2007, 00:37

bmwhype2 wrote:

sqrt 3.

let midpoint of EH = M
let midpoint of AB = N
Drop perpendicular from M to side AD on F
AN = (sqrt 2)/2
AF = (sqrt 2)/2
FN = [(sqrt 2)/2]^2 + [(sqrt 2)/2]^2 = 1
MN^2 = 1^2 + (sqrt 2)^2 = 3
MN = sqrt 3

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[#permalink]

27 Nov 2007, 03:45

haha! I guesstimated D.

Midpoint AB=M1
Midpoint EF=M2
Midpoint EH=M3

Segment M1M2=sqrt2, hence, M1M3 had to be bigger than that.

Eliminate A, B, C.

Down to D, E. E = 2*1.7*=3.4, which is more than 2 times the segment between M1-M2. No way. D is the only one 8-)

Now, I'll learn how to solve it properly!

[#permalink] 27 Nov 2007, 03:45

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Square ABCD is the base of the cube while square EFGH is the

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Square ABCD is the base of the cube while square EFGH is the

Square ABCD is the base of the cube while square EFGH is the

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