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# In a certain type of tiling called Penrose P3 tiling, two ty

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In a certain type of tiling called Penrose P3 tiling, two ty [#permalink]

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28 Apr 2013, 23:05
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In a certain type of tiling called Penrose P3 tiling, two types of rhombi fill a space without gaps or overlaps: wide rhombi and narrow rhombi. If five of the wide rhombi can meet symmetrically at a single point, while ten of the narrow rhombi can, what is the ratio of the largest angle in one narrow rhombus to the largest angle in one wide rhombus?

(A) 5 : 2
(B) 2 : 1
(C) 5 : 3
(D) 3 : 2
(E) 4 : 3
[Reveal] Spoiler: OA

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Last edited by emmak on 05 May 2013, 23:13, edited 1 time in total.

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Re: In a certain type of tiling called Penrose P3 tiling, two ty [#permalink]

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28 Apr 2013, 23:28
Hello Emmak

Since 5 Wide Rhombi can meet at any given point there fore the concerned angle of the rhombus must be 360/5 = 72deg.
The wider angle will be 180-72 (as the sum of adjacent angles is always 180deg. in any parallelogram) = 108deg.

In case of the narrow Rhombi since 10 can meet therefore the angle will be 36deg. and the wider angle is 144deg.

So ratio is 144/108 = 4/3 that is E
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Re: In a certain type of tiling called Penrose P3 tiling, two ty [#permalink]

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28 Apr 2013, 23:40
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5 wide rhombi can meet symmetrically at a single point, therefore one angle of each wide rhombi = 360/5 = 72
Similarly, as 10 narrow rhombi meet symmetrically at a single point, therefore one angle of each narrow rhombi = 360/10 = 36

Since, opp. angles of a rhombi are equal, and total measure of interior angles of a rhombi is 360

For a wide rhombi, measures of 4 angles = 72,72,x,x
Therefore, 72+72+x+x=360, i.e 2x=360-144=216 , i.e x =108

For a narrow rhombi, measures of 4 angles = 36,36,y,y
Therefore, 36+36+y+y=360, i.e 2y=360-72=288 , i.e y =144

Ratio of the largest angle in one narrow rhombus to the largest angle in one wide rhombus
y:x = 144:108 = 4:3

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Re: In a certain type of tiling called Penrose P3 tiling, two ty [#permalink]

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01 May 2013, 05:05
karishmatandon wrote:
5 wide rhombi can meet symmetrically at a single point, therefore one angle of each wide rhombi = 360/5 = 72
Similarly, as 10 narrow rhombi meet symmetrically at a single point, therefore one angle of each narrow rhombi = 360/10 = 36

Since, opp. angles of a rhombi are equal, and total measure of interior angles of a rhombi is 360

For a wide rhombi, measures of 4 angles = 72,72,x,x
Therefore, 72+72+x+x=360, i.e 2x=360-144=216 , i.e x =108

For a narrow rhombi, measures of 4 angles = 36,36,y,y
Therefore, 36+36+y+y=360, i.e 2y=360-72=288 , i.e y =144

Ratio of the largest angle in one narrow rhombus to the largest angle in one wide rhombus
y:x = 144:108 = 4:3

Hi,
I see that you have got the answer, pls can you help in explaining the question in detail ? I am not able to comprehend what the question wants to say ?

Best--

Ankit !!

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Re: In a certain type of tiling called Penrose P3 tiling, two ty [#permalink]

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01 May 2013, 05:21
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ankit546 wrote:
Hi,
I see that you have got the answer, pls can you help in explaining the question in detail ? I am not able to comprehend what the question wants to say ?

Best--

Ankit !!

Hi ankit546, you may wanna take a look at this

The largest angle in one wide rhombus is $$180-72=108$$

The largest angle in one narrow rhombus is $$180-36=144$$

Ratio $$\frac{144}{108}=\frac{4}{3}$$
Hope this helps, let me know
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Re: In a certain type of tiling called Penrose P3 tiling, two ty [#permalink]

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01 May 2013, 06:22
Zarrolou wrote:
ankit546 wrote:
Hi,
I see that you have got the answer, pls can you help in explaining the question in detail ? I am not able to comprehend what the question wants to say ?

Best--

Ankit !!

Hi ankit546, you may wanna take a look at this

The largest angle in one wide rhombus is $$180-72=108$$

The largest angle in one narrow rhombus is $$180-36=144$$

Ratio $$\frac{144}{108}=\frac{4}{3}$$
Hope this helps, let me know

Hi,

The drawing that you shared cleared the question. I was getting all confused with this wide rhombi narrow rhombi.
After looking at the pic I know where I went wrong.

Thanks Zarrolou

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Re: In a certain type of tiling called Penrose P3 tiling, two ty [#permalink]

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13 Nov 2017, 06:04
emmak wrote:
In a certain type of tiling called Penrose P3 tiling, two types of rhombi fill a space without gaps or overlaps: wide rhombi and narrow rhombi. If five of the wide rhombi can meet symmetrically at a single point, while ten of the narrow rhombi can, what is the ratio of the largest angle in one narrow rhombus to the largest angle in one wide rhombus?

(A) 5 : 2
(B) 2 : 1
(C) 5 : 3
(D) 3 : 2
(E) 4 : 3

I think the question must specify more details. Each of the wide rhombus and narrow rhombus will have two different angles, one big and one small. It must be specified from which end are the rhombii meeting symmetrically, from the big angle portion or the small angle portion. Bunuel If my reasoning is incorrect, please explain.
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Re: In a certain type of tiling called Penrose P3 tiling, two ty   [#permalink] 13 Nov 2017, 06:04
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# In a certain type of tiling called Penrose P3 tiling, two ty

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