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# If the three regular polygons in the figure above have equal perimeter

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Math Expert
Joined: 02 Sep 2009
Posts: 46217
If the three regular polygons in the figure above have equal perimeter [#permalink]

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20 Sep 2017, 23:01
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Question Stats:

83% (00:45) correct 17% (00:49) wrong based on 35 sessions

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If the three regular polygons in the figure above have equal perimeters, which of the following is true?

(A) s < t < p
(B) s < p < t
(C) r < p < t
(D) p < t < s
(E) p < s < t

Attachment:

2017-09-20_1022_003.png [ 11.76 KiB | Viewed 634 times ]

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Joined: 02 Jul 2017
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Re: If the three regular polygons in the figure above have equal perimeter [#permalink]

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20 Sep 2017, 23:13
By figure perimeters are equal :

4s = 3t= 5p

=> $$t = \frac{4}{3}s$$ and $$s =\frac{5}{4}p$$
=> p<s<t

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Joined: 06 Aug 2017
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Re: If the three regular polygons in the figure above have equal perimeter [#permalink]

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20 Sep 2017, 23:26
Bunuel wrote:

If the three polygons in the figure above have equal perimeters, which of the following is true?

(A) s < t < p
(B) s < p < t
(C) r < p < t
(D) p < t < s
(E) p < s < t

Attachment:
2017-09-20_1022_003.png

Hi Bunuel,

Since it is mentioned in the image that "Figure not drawn to scale", please confirm if the polygons are to be considered "Regular"?
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Math Expert
Joined: 02 Sep 2009
Posts: 46217
Re: If the three regular polygons in the figure above have equal perimeter [#permalink]

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20 Sep 2017, 23:29
Jabjagotabhisavera wrote:
Bunuel wrote:

If the three polygons in the figure above have equal perimeters, which of the following is true?

(A) s < t < p
(B) s < p < t
(C) r < p < t
(D) p < t < s
(E) p < s < t

Attachment:
2017-09-20_1022_003.png

Hi Bunuel,

Since it is mentioned in the image that "Figure not drawn to scale", please confirm if the polygons are to be considered "Regular"?

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Yes.
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Re: If the three regular polygons in the figure above have equal perimeter [#permalink]

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20 Sep 2017, 23:40
Since perimeters are equal
4s = 3t = 5p
s = 0.75t
p = 0.6t
So s:p:t = 0.75:0.6:1
Hence p<s<t

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If the three regular polygons in the figure above have equal perimeter [#permalink]

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21 Sep 2017, 18:17
Bunuel wrote:

If the three regular polygons in the figure above have equal perimeters, which of the following is true?

(A) s < t < p
(B) s < p < t
(C) r < p < t
(D) p < t < s
(E) p < s < t

Attachment:
2017-09-20_1022_003.png

Pick a smart number for the perimeter that is a multiple of 4, 3, and 5 (the number of sides, respectively, of the figures).

Let the perimeter for all equal 60. To get side lengths, divide perimeter by # of sides

s = 60/4 = 15
t = 60/3 = 20
p = 60/5 = 12

p < s < t

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If the three regular polygons in the figure above have equal perimeter   [#permalink] 21 Sep 2017, 18:17
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