Final answer:
To solve the problem, we use the given formula P = 11L - 42 and the perimeter of a square P = 4L to set up and solve the equation 4L = 11L - 42, which simplifies to L = 6. Thus, the length of a side of the square is 6 units.
Step-by-step explanation:
The question asks us to find the length of a side of a square given that the perimeter (P) is 11 times the length of a side (L), decreased by 42: P = 11L - 42. Considering the formula for the perimeter of a square, P = 4L, we can set up an equation:
4L = 11L - 42.
To solve for L, we move all the terms involving L to one side of the equation:
4L - 11L = -42
-7L = -42
Dividing both sides by -7 to isolate L:
L = 6
Therefore, the length of a side of the square is 6 units.