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# ABCDEFGH is a cube. What is the length of the line segment AG ?

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Math Expert
Joined: 02 Sep 2009
Posts: 44298
ABCDEFGH is a cube. What is the length of the line segment AG ? [#permalink]

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22 Oct 2017, 06:46
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Difficulty:

25% (medium)

Question Stats:

94% (00:22) correct 6% (00:00) wrong based on 35 sessions

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ABCDEFGH is a cube. What is the length of the line segment AG ?

(1) The length of the line segment AB is 4 inches.
(2) The area of the square BCGH is 16 square inches

[Reveal] Spoiler:
Attachment:

2017-10-22_1743_001.png [ 8.71 KiB | Viewed 822 times ]
[Reveal] Spoiler: OA

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ABCDEFGH is a cube. What is the length of the line segment AG ? [#permalink]

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22 Oct 2017, 09:27

In the given figure of the cube, we have been
asked to find the length of the diagonal of the cube.

Cube - Formulae
Diagonal - Side$$\sqrt{3}$$
Area - $$Side^2$$

The first statement explicitly gives us length of a side,
from which we can deduce the length of diagonal
Similarly, the second statement give us the area of the cube,
using which we can find the length of the cube with which
you can find the length of the diagonal. (Option D)
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Re: ABCDEFGH is a cube. What is the length of the line segment AG ? [#permalink]

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22 Oct 2017, 09:41
pushpitkc wrote:

Diagonal - Side$$\sqrt{2}$$

Small correction - Cube diagonal (AG) is $$\sqrt{3}$$ * Side
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Re: ABCDEFGH is a cube. What is the length of the line segment AG ? [#permalink]

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22 Oct 2017, 09:45
Line segment AG is the diagonal of the cube
Diagonal of cube = $$\sqrt{3}$$ * Side
S1 - AB=4
Side is given, diagonal can be found. Sufficient.

S2 - Area BCGH=16.
Side = $$\sqrt{16}$$=4
Sufficient.

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Re: ABCDEFGH is a cube. What is the length of the line segment AG ? [#permalink]

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23 Oct 2017, 17:20
Bunuel wrote:

ABCDEFGH is a cube. What is the length of the line segment AG ?

(1) The length of the line segment AB is 4 inches.
(2) The area of the square BCGH is 16 square inches

[Reveal] Spoiler:
Attachment:
2017-10-22_1743_001.png

Question is about Diagonal of the cube = ??

Statement 1- length of line segment is given. So, diagonal of cube can be calculated.
Statement 2- from area of square BCGH, we can calculate length of line segment, So, we can calculate diagonal of cube can be calculated.

Re: ABCDEFGH is a cube. What is the length of the line segment AG ?   [#permalink] 23 Oct 2017, 17:20
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