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A window is in the shape of a regular hexagon with each side of length
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22 Dec 2015, 10:59
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78% (01:06) correct 22% (01:36) wrong based on 533 sessions
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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
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25 Dec 2015, 11:10
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. GMAT assassins aren't born, they're made, Rich
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A window is in the shape of a regular hexagon with each side of length
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26 May 2016, 14:25
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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Re: A window is in the shape of a regular hexagon with each side of length
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26 May 2016, 00:57
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 [ 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 306090 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
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26 May 2016, 01:06
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, Nalin



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Re: A window is in the shape of a regular hexagon with each side of length
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26 May 2016, 01:14



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Re: A window is in the shape of a regular hexagon with each side of length
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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
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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
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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
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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
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18 Oct 2018, 13:16
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