Question

The sides of a regular hexagon are equal in length. The perimeter of the hexagon is at most 24 inches. Find the possible side lengths of the hexagon. Let the lengths of the sides be x.

Answer 1

`0 < \text{x} \le 4`

If x is an integer, then x is any value in the set {1,2,3,4}

======================================================

Work Shown:

x = length of each side

6x = perimeter of the regular hexagon

The perimeter must be greater than 0.

Also, the perimeter must be less than or equal to 24. This is because of the phrasing "perimeter is at most 24 inches".

In other words, the perimeter is between 0 and 24, excluding 0 and including 24.

`0 < \text{ perimeter } \le 24\\\\0 < 6\text{x} \le 24\\\\0/6 < 6\text{x}/6 \le 24/6\\\\0 < \text{x} \le 4\\\\`

If x is an integer, then x can be any value in the set {1,2,3,4}

Examples:

• The side length x = 2 leads to a perimeter 6x = 6*2 = 12 inches. This shows why x = 2 is in the set shown above.
• The side length x = 5 leads to a perimeter 6x = 6*5 = 30 inches. This shows why x = 5 (and larger) is not in the set shown above.