The perimeter of the polygon is 232 units
Perimeter of a polygon
From the question, we are to determine the perimeter of the regular polygon
From the diagram,
One of the polygon's side length is (4/3)x - 1/3
and another side length is x + 7
Since the figure is a regular polygon, we can write that
(4/3)x - 1/3 = x + 7
Now, solve for x
(4/3)x - 1/3 = x + 7
Multiply through by 3
4x - 1 = 3x + 21
4x - 3x = 21 + 1
x = 22
One of the polygon's side length is x + 7
∴ One side length = 22 + 7
One side length = 29
Since the polygon has 8 sides,
The perimeter of the polygon will be
8 × 29
= 232 units
Hence, the perimeter of the polygon is 232 units
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