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If a regular hexagon is drawn in a square of side 12 em, such that the
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CaptainLevi
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If a regular hexagon is drawn in a square of side 12 em, such that the [#permalink] New post  25 Nov 2019, 00:58
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If a regular hexagon is drawn in a square of side 12 cm, such that there is at least one vertex of the hexagon on each side of the square, what is the side of the regular hexagon that is drawn?

(A) \(4\sqrt{3}\) cm
(B) 6 cm
(C) \(6(\sqrt{6} - \sqrt{2})\)cm
(D) \(6(\sqrt{6}-\sqrt{3})\)cm
(E) \(6(\sqrt{7}-\sqrt{5})\)cm
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Keshav9636
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Re: If a regular hexagon is drawn in a square of side 12 em, such that the [#permalink] New post  25 Nov 2019, 01:45
Can someone please solve this? I am not able to decode the question. Answers that I am getting are nowhere near the solution.
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siddharthfrancis
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Re: If a regular hexagon is drawn in a square of side 12 em, such that the [#permalink] New post  23 Dec 2019, 06:16
can anyone explain this
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nick1816
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Joined: 19 Oct 2018
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Re: If a regular hexagon is drawn in a square of side 12 em, such that the [#permalink] New post  23 Dec 2019, 08:13
Not a GMAT question IMO

Triangle FWA is 45-90-45

Hence, \(x= \sqrt{2}a\)......(1)

In triangle BAX

\(\frac{x}{sin(45)}= \frac{12-a}{sin(120)}\)

\(\sqrt{2}x= \frac{2*(12-a)}{\sqrt{3}}\)

From (1)

\(2a= \frac{2*(12-a)}{\sqrt{3}}\)

\(\sqrt{3}a= 12-a\)

\(a= \frac{12}{\sqrt{3}+1}\)

\(a= 6*(\sqrt{3}-1)\)

Length of side of regular hexagon

= \(\sqrt{2}a\)

= \(\sqrt{2}*6*(\sqrt{3}-1)\)

= \(6(\sqrt{6} - \sqrt{2})\)


CaptainLevi wrote:
If a regular hexagon is drawn in a square of side 12 cm, such that there is at least one vertex of the hexagon on each side of the square, what is the side of the regular hexagon that is drawn?

(A) \(4\sqrt{3}\) cm
(B) 6 cm
(C) \(6(\sqrt{6} - \sqrt{2})\)cm
(D) \(6(\sqrt{6}-\sqrt{3})\)cm
(E) \(6(\sqrt{7}-\sqrt{5})\)cm

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jhodge
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Re: If a regular hexagon is drawn in a square of side 12 em, such that the [#permalink] New post  23 Dec 2019, 09:40
Is something like this really going to show up on the gmat???
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nick1816
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Joined: 19 Oct 2018
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Re: If a regular hexagon is drawn in a square of side 12 em, such that the [#permalink] New post  23 Dec 2019, 10:14
It can show up as the 31st question, if you attempt first 30 correctly. Just kidding. It's hard to solve this question in 2 minutes without trigonometry. {GMAC doesn't test Trigno in particular.}

jhodge wrote:
Is something like this really going to show up on the gmat???
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