BTGmoderatorLU 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 any number from?
A. 3 to 6
B. 4 to 5
C. 3 to 7
D. 4 to 6
E. 4 to 7
The OA is D.
Please, can someone explain this PS question? I'm confused about how can I solve it. Thanks in advance!
Given: The perimeter of a polygon is 16. 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.
To find out: Possible number of sides of the polygon.
Say the polygon has n sides; thus, we have to find out the minimum and the maximum value of n.
Since the perimeter is 16, the shortest side of the polygon is 2, and the longest side of the polygon is 5, the sum of the remaining (n - 2) sides = 16 - 2 - 5 = 9.
Case 1: Finding the minimum value of n
To find the minimum value of n, we must assume that the remaining (n - 2) sides are of 5 units (maximum possible dimension) each.
=> 9 = 5*(n - 2) => n = 3.8
Since n is an integer, the minimum value of n is 4.
Case 2: Finding the maximum value of n
To find the maximum value of n, we must assume that the remaining (n - 2) sides are of 2 units (minimum possible dimension) each.
=> 9 = 2*(n - 2) => n = 6.5
Since n is an integer, the maximum value of n is 6.
The correct answer:
D
Hope this helps!
-Jay
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