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A window is in the shape of a regular hexagon with each side of length

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A window is in the shape of a regular hexagon with each side of length  [#permalink]

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New post 22 Dec 2015, 10:59
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A window is in the shape of a regular hexagon with each side of length 80 Centimeters. If a diagonal through the center of the hexagon is W centimeters long, then w =?

(A) 80
(B) 120
(C) 150
(D) 160
(E) 240
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Re: A window is in the shape of a regular hexagon with each side of length  [#permalink]

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New post 25 Dec 2015, 11:10
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Hi kkahuja91,

I'm going to give you a couple of hints so that you can attempt this question again on your own:

1) A regular hexagon has 6 equal sides and 6 equal angles (that are all 120 degrees).
2) You can 'cut' a regular hexagon into 6 equal EQUILATERAL triangles. If you know how to calculate the height of an equilateral triangle, then you should be able to answer this question.

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A window is in the shape of a regular hexagon with each side of length  [#permalink]

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New post 26 May 2016, 14:25
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A regular hexagon consists of six identical equilateral triangles,
each of whose sides is 80 cm.
We know the triangles are equilateral because each of
the 3 diagonals that run through the center bisects the
regular hexagon's internal 120°∠ into two 60° ∠s.
Therefore, w=(2)(80)=160 cm.
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hexagon.jpg
hexagon.jpg [ 14.24 KiB | Viewed 8872 times ]

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Re: A window is in the shape of a regular hexagon with each side of length  [#permalink]

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New post 26 May 2016, 00:57
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kkahuja91 wrote:
A window is in the shape of a regular hexagon with each side of length 80 Centimeters. If a diagonal through the center of the hexagon is W centimeters long, then w =?

(A) 80
(B) 120
(C) 150
(D) 160
(E) 240


Attachment:
Solution.png
Solution.png [ 8.02 KiB | Viewed 9022 times ]


Let us draw a regular hexagon ABCDEF, as in figure above. We need to find the length of the diagonal BE.
Given: It is a regular hexagon so, AB = BC = CD = DE = EF = AF = 80 cm and each angle is 120
Join BF and CE, making BCEF a rectangle. Angle BCE = 90
As the diagonal BE bisects angles ABC and DEF, angle CBE is 60. So, triangle BCE is a 30-60-90 triangle and the sides of this triangle is in the ratio - \(1:\sqrt{3}:2\)
Hence, BE = 160
Answer - D.
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Re: A window is in the shape of a regular hexagon with each side of length  [#permalink]

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New post 26 May 2016, 01:06
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Dear Moderators,

The source of this question is mentioned as Manhattan GMAT. This is actually from Official Guide Quant Review 2016 (PS# 145). Request you to change it.

Thanks,
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Re: A window is in the shape of a regular hexagon with each side of length  [#permalink]

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Re: A window is in the shape of a regular hexagon with each side of length  [#permalink]

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New post 16 Aug 2016, 05:32
Bunuel I didn't get the below part. how does diagonal BE bisects angle ABC and DEF

Quote:
diagonal BE will bisects angles ABC and DEF, angle CBE is 60.

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Re: A window is in the shape of a regular hexagon with each side of length  [#permalink]

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New post 17 Aug 2016, 20:28
kapru wrote:
I didn't get the below part. how does diagonal BE bisects angle ABC and DEF

Quote:
diagonal BE will bisects angles ABC and DEF, angle CBE is 60.


" If a diagonal through the center of the hexagon is W centimeters long" -- this part of the question tells you there's a bisecting line (i.e. it's sliced down the middle).
Because each angle of a hexagon is 120 degrees.. bisecting it results in 60 degrees on each side.
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A window is in the shape of a regular hexagon with each side of length  [#permalink]

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New post 09 Oct 2017, 11:55
kkahuja91 wrote:
A window is in the shape of a regular hexagon with each side of length 80 Centimeters. If a diagonal through the center of the hexagon is W centimeters long, then w =?

(A) 80
(B) 120
(C) 150
(D) 160
(E) 240


Triangle in the hexagon is equilateral; you know it is equilateral because the degree of one of its angles is 60; you know it is 60, because the sum degrees of a hexagon is 720; 720/6 = 120 degrees per angle in hexagon; the triangle's sides splits that 120 degree hexagon angle in half, making 60 degrees.

The triangle is equilateral; all sides equal each other. therefore, BC = AB = 80. The question asks for diagonal, meaning the line cuts all the way through the hexagon - you have to double BC.

therefore, given BC = 80, 80 x 2 = 160 cm
Answer (D) 160
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Re: A window is in the shape of a regular hexagon with each side of length  [#permalink]

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New post 12 Oct 2017, 17:09
kkahuja91 wrote:
A window is in the shape of a regular hexagon with each side of length 80 Centimeters. If a diagonal through the center of the hexagon is W centimeters long, then w =?

(A) 80
(B) 120
(C) 150
(D) 160
(E) 240


When the hexagon is broken up by 6 diagonals, 6 equilateral triangles are created. Since each side of the hexagon is 80 cm and the length of 1 diagonal is 2 times the length of a side of the hexagon, we have 2 x 80 = 160. Thus, w = 160.

Answer: D
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Re: A window is in the shape of a regular hexagon with each side of length  [#permalink]

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