232
The picture is of an 8 sided polygon. One of the sides is labeled with the length (4/3)x -1/3, another side is labeled with the length x+7. Since both sides are the same length, create an equation setting them against each other.
(4/3)x - 1/3 = x + 7
Subtract 7 from both sides
(4/3)x - 1/3 - 7 = x
Subtract (4/3)x from both sides
-7 1/3 = x - (4/3)x
-7 1/3 = -(1/3)x
Divide both sides by -(1/3)
-7 1/3 / (-1/3) = x
-22/3 * (-3/1) = x
22 = x
So we now know that x = 22.
Now calculate the length of a side.
x + 7 = 22 + 7 = 29
(4/3)x - 1/3 = (4/3)22 - 1/3 = 29 1/3 - 1/3 = 29
Both expressions for length agree on a length of 29.
Since the polygon has 8 sides and every side has the same length, the perimeter of the polygon is 8 * 29 = 232.
