Let's denote the length of a side of the square plywood platform as "S."
The perimeter of a square is the sum of all its sides, so the perimeter of this square can be expressed as
Perimeter = 4S
According to the problem, the perimeter is 11 times the length of a side, decreased by 28:
Perimeter = 11S - 28
Now, we can set these two expressions for the perimeter equal to each other because they represent the same value:
4S = 11S - 28
To solve for S (the length of a side), you can start by moving 4S to the right side of the equation by adding 4S to both sides:
4S + 4S = 11S - 28 + 4S
This simplifies to:
8S = 11S - 28
Now, subtract 11S from both sides:
8S - 11S = 11S - 11S - 28
This simplifies to:
-3S = -28
Finally, divide both sides by -3 to find the length of a side (S):
S = (-28) / (-3)
S = 28 / 3
Simplify the fraction:
S = 9.33 (rounded to two decimal places)
So, the length of a side of the square plywood platform is approximately 9.33 units.