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The perimeter of a polygon is 16. If the sides of the polygon are all

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Bunuel
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The perimeter of a polygon is 16. If the sides of the polygon are all [#permalink] New post   20 Apr 2021, 01:30
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The perimeter of a polygon is 16. If the sides of the polygon are all of integer length, the shortest side of the polygon is 2 and the longest side of the polygon is 5, then the number of sides of the polygon could be any number from

A. 3 to 6
B. 4 to 5
C. 3 to 7
D. 4 to 6
E. 4 to 7


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D
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The perimeter of a polygon is 16. If the sides of the polygon are all [#permalink] New post   20 Apr 2021, 06:37
The perimeter of a polygon is 16. If the sides of the polygon are all of integer length, the shortest side of the polygon is 2 and the longest side of the polygon is 5, then the number of sides of the polygon could be any number from

A. 3 to 6
B. 4 to 5
C. 3 to 7
D. 4 to 6
E. 4 to 7

Let sides be A1,A2,A3........
16=2+5+A1+A2.....
9 =A1+A2...........
Since shortest side is 2 and longest is 5, 2<= A<=5 ( other sides are any number from 2 to 5)
possible combinations are
4+5 +2+5 = 16
5+2+2+2+5 =16
3+2+2+2+2+5 = 16

no of sides can be 4 to 6 Ans is D
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Re: The perimeter of a polygon is 16. If the sides of the polygon are all [#permalink] New post   20 Apr 2021, 09:23
Bunuel wrote:
The perimeter of a polygon is 16. If the sides of the polygon are all of integer length, the shortest side of the polygon is 2 and the longest side of the polygon is 5, then the number of sides of the polygon could be any number from

A. 3 to 6
B. 4 to 5
C. 3 to 7
D. 4 to 6
E. 4 to 7

2 sides are 2 and 5 = 7
Remaining sides = 16-7 = 9

Minimum sides = 5 & 4 so total = 2+2 = 4
Maximum sides = 2, 2, 2, 3 so total = 4+2 = 6

Ans: 4 to 6 = D
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Re: The perimeter of a polygon is 16. If the sides of the polygon are all [#permalink] New post   20 Apr 2021, 09:36
The perimeter of a polygon is 16. If the sides of the polygon are all of integer length, the shortest side of the polygon is 2 and the longest side of the polygon is 5, then the number of sides of the polygon could be any number from

2 +...........+ 5 = 16 So, we need fill sides with 16- 7= 9 length = 4+5. So. min sides of polygon = 4
For max sides of polygon = 2+ 2+2+2+3 +5 = 6 sides

So, I think D. :)
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Re: The perimeter of a polygon is 16. If the sides of the polygon are all [#permalink] New post   20 Apr 2021, 13:25
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Shortest side = 2
Longest side = 5

Perimeter left = 16 - 7 = 9

9 has to be distributed as sum of integers greater than or equal to 2 and less than or equal to 5

So, 9 = 2,2,2,3 (No. of sides = 6)
or 9 = 5,4 (No. of sides = 4)

Ans D
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Re: The perimeter of a polygon is 16. If the sides of the polygon are all [#permalink] New post   16 May 2021, 07:45
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Bunuel wrote:
The perimeter of a polygon is 16. If the sides of the polygon are all of integer length, the shortest side of the polygon is 2 and the longest side of the polygon is 5, then the number of sides of the polygon could be any number from

A. 3 to 6
B. 4 to 5
C. 3 to 7
D. 4 to 6
E. 4 to 7



Solution:

Since two of the sides have a total length of 2 + 5 = 7, the remaining sides have a total length of 16 - 7 = 9.

Since no side is longer than 5, we could have two more sides to make up the total length of the remaining side (e.g., 4 + 5 = 9). Therefore, the least number of sides the polygon could have is 4.

Similarly, since no side is shorter than 2, we could have four more sides to make up the total length of the remaining side (e.g., 2 + 2 + 2 + 3 = 9). Therefore, the greatest number of sides the polygon could have is 6.

Answer: D
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Re: The perimeter of a polygon is 16. If the sides of the polygon are all [#permalink]
16 May 2021, 07:45
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