Final answer:
The perimeter of a regular polygon is the length of one side multiplied by the number of sides. Upon solving the equation for x, we find that the length of one side is 28 2/3 meters. Without the number of sides, we cannot determine the perimeter from the given options.
Step-by-step explanation:
To find the perimeter of a regular polygon, where each side has the same length, we first need to solve the equation ({4}/{3}x - {1}/{3} = x + 7) for x. This will give us the length of one side of the polygon.
Let's solve the equation:
- Multiply both sides by 3 to eliminate the fractions: 4x - 1 = 3x + 21.
- Subtract 3x from both sides: x - 1 = 21.
- Add 1 to both sides: x = 22.
Now, if each side of the polygon is ({4}/{3}x - {1}/{3}), we substitute the value of x to find the length of one side:
Length of one side = ({4}/{3})(22) - {1}/{3} = 29 - {1}/{3} = 282/3 meters.
The polygon is regular, which means all its sides are equal. If it has n sides, the perimeter (P) would be P = n × length of one side.
Since we don't know the number of sides n, we cannot determine the exact perimeter. However, choice (a) represents the length of one side, and not the perimeter. Choice (b) represents a value we found earlier during the solution, and is not related to the side length or the perimeter. Choices (c) and (d) are not related to the original problem as presented.
Thus, without the number of sides n, we cannot select the correct option for the perimeter among the ones given.