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Square ABCD is the base of the cube while square EFGH is the [#permalink]
26 Nov 2007, 23:24

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Difficulty:

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Question Stats:

64% (03:27) correct
36% (01:57) wrong based on 167 sessions

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?

A. \(\frac{1}{\sqrt{2}}\) B. 1 C. \(\sqrt{2}\) D. \(\sqrt{3}\) E. \(2\sqrt{3}\)

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.

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.

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.

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

Re: Square ABCD is the base of the cube while square EFGH is the [#permalink]
29 May 2014, 04:46

I used deluxe pythag to solve....

We know that the area of the square is 2, therefore the side = sqrt2 or 2^1/2. We know the midpoints are (2^1/2)/2.

So in reality, we are just finding the main diagonal of a rectangular solid with lengths (2^1/2)/2, (2^1/2)/2, and (2^1/2); apply deluxe pythag theorum.

Find x - Main diagonal ((2^1/2)/2)^2 + ((2^1/2)/2)^2 + (2^1/2)^2 = x^2 (2/2)+(2/2)+2=x^2 1/2+1/2+2=x^2 3=x^2 3^1/2=x

Re: Square ABCD is the base of the cube while square EFGH is the [#permalink]
29 May 2014, 05:45

Expert's post

1

This post was BOOKMARKED

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?

A. \(\frac{1}{\sqrt{2}}\) B. 1 C. \(\sqrt{2}\) D. \(\sqrt{3}\) E. \(2\sqrt{3}\)

Look at the diagram below:

Attachment:

Cube.png [ 14.44 KiB | Viewed 1698 times ]

Notice that Z is the midpoint of AD. We need to find the length of line segment XY.

Now, since the area of ABCD is 2 then each edge of the cube equals to \(\sqrt{2}\).

Re: Square ABCD is the base of the cube while square EFGH is the [#permalink]
16 Jun 2014, 05:10

Why angle Z is the right angle?

Bunuel wrote:

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?

A. \(\frac{1}{\sqrt{2}}\) B. 1 C. \(\sqrt{2}\) D. \(\sqrt{3}\) E. \(2\sqrt{3}\)

Look at the diagram below:

Attachment:

Cube.png

Notice that Z is the midpoint of AD. We need to find the length of line segment XY.

Now, since the area of ABCD is 2 then each edge of the cube equals to \(\sqrt{2}\).

Re: Square ABCD is the base of the cube while square EFGH is the [#permalink]
16 Jun 2014, 05:42

Expert's post

amar13 wrote:

Why angle Z is the right angle?

Bunuel wrote:

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?

A. \(\frac{1}{\sqrt{2}}\) B. 1 C. \(\sqrt{2}\) D. \(\sqrt{3}\) E. \(2\sqrt{3}\)

Look at the diagram below:

Attachment:

Cube.png

Notice that Z is the midpoint of AD. We need to find the length of line segment XY.

Now, since the area of ABCD is 2 then each edge of the cube equals to \(\sqrt{2}\).

Re: Square ABCD is the base of the cube while square EFGH is the [#permalink]
28 Jun 2015, 10:13

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Re: Square ABCD is the base of the cube while square EFGH is the [#permalink]
01 Jul 2015, 04:52

Bunuel wrote:

amar13 wrote:

Why angle Z is the right angle?

Bunuel wrote:

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?

A. \(\frac{1}{\sqrt{2}}\) B. 1 C. \(\sqrt{2}\) D. \(\sqrt{3}\) E. \(2\sqrt{3}\)

Look at the diagram below:

Attachment:

Cube.png

Notice that Z is the midpoint of AD. We need to find the length of line segment XY.

Now, since the area of ABCD is 2 then each edge of the cube equals to \(\sqrt{2}\).

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