Answer: The length of a side equals 3 units.
Step-by-step explanation: The given figure is a square, and a square is a shape with all four sides having equal measurement. This means if the length is given as L, then the width would also measure as L.
Also we are given a clue as to the measurement of the perimeter of the square. Normally, the perimeter of a square would be computed as
Perimeter = 4L (that is, add up all four sides). But since we have been told that the perimeter is equal to eight times the length of a side {8 x L, or 8L} decreased by 12 {8L - 12} we can conveniently express the perimeter as
Perimeter = 8L - 12.
However, remember that the formula for a perimeter is Perimeter = 4L. Therefore what we have come up with is,
8L - 12 = 4L
(Remember that both sides of the equation represents the perimeter)
By collecting like terms we now have
8L - 4L = 12
(Remember that when a negative value crosses from one side of the equation to the other, it becomes positive, and vice versa)
8L - 4L = 12
4L = 12
Divide both sides of the equation by 4
L = 3
Therefore, one side of the square measures 3 units
