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The perimeter of a polygon with sides of integer length is 45. If the

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Bunuel
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The perimeter of a polygon with sides of integer length is 45. If the [#permalink] New post   07 May 2021, 05:15
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The perimeter of a polygon with sides of integer length is 45. If the smallest side of the polygon is 5 and the longest side of the polygon is 10, then the number of sides could be any number from

A. 5 to 7
B. 5 to 8
C. 5 to 9
D. 6 to 8
E. 6 to 9
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Bunuel
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Re: The perimeter of a polygon with sides of integer length is 45. If the [#permalink] New post   08 May 2021, 08:45
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Bunuel wrote:
The perimeter of a polygon with sides of integer length is 45. If the smallest side of the polygon is 5 and the longest side of the polygon is 10, then the number of sides could be any number from

A. 5 to 7
B. 5 to 8
C. 5 to 9
D. 6 to 8
E. 6 to 9


The sum of the length of the remaining sides must be 45 - (5 + 10) = 30.

We can have 5-sided polygon {5, 10, 10, 10, 10} (we cannot increase the length of any side to reduce the number of sides);
We can have 6-sided polygon {5, 5, 5, 10, 10, 10};
We can have 7-sided polygon {5, 5, 5, 5, 5, 10, 10};
We can have 8-sided polygon {5, 5, 5, 5, 5, 5, 5, 10} (we cannot decrease the length of any side to increase the number of sides).

Answer: B.
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Re: The perimeter of a polygon with sides of integer length is 45. If the [#permalink] New post   07 May 2021, 05:40
Shortest side: 5
Longest side: 10
Perimeter: 45

As 2 sides are given, the remaining sides must sum to 30.

The most amount of sides will be when all of the other sides are equal to the shortest side. 30/5 = 6
6 plus the 2 given sides = 8 sides

The least amount of sides will be when all of the other sides are equal to the longest side. 30/10 = 3
3 plus the 2 given sides = 5 sides

so range is between 5 and 8

Answer B
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Re: The perimeter of a polygon with sides of integer length is 45. If the [#permalink] New post   08 May 2021, 09:01
The perimeter of a polygon with sides of integer length is 45. If the smallest side of the polygon is 5 and the longest side of the polygon is 10, then the number of sides could be any number from

For min nos. of side = 5.......10, we need rest of 30 to be divided by 10. So, Total sides = 2+ 3= 5
For max nos. of side = 5.......10, we need rest of 30 to be divided by 5. So, Total sides = 2+ 6= 8

So, It is B. :)
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Re: The perimeter of a polygon with sides of integer length is 45. If the [#permalink] New post   09 May 2021, 00:24
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Smallest side: 5
Longest side: 10

Perimeter: 45

Remaining side sum: 45 - 15 = 30

Now. if we have 9 sides polygon then 9 - 2 = 7 cannot make sum = 30 because if all sides are 5 units, then 6 sides will give us the sum as 30 and we will be still left with 1 side.

If we have 5 sides polygon then 5 - 2 = 3 can make sum = 30 [10,10,10]
If we have 6 sides polygon then 6 - 2 = 4 can make sum = 30 [5,5,10,10]
If we have 7 sides polygon then 7 - 2 = 5 can make sum = 30 [5, 5, 5, 5,10]
If we have 6 sides polygon then 8 - 2 = 6 can make sum = 30 [5, 5, 5, 5, 5, 5]

Range of sides 5 to 8.

Answer B
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Re: The perimeter of a polygon with sides of integer length is 45. If the [#permalink]
09 May 2021, 00:24
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