A square plywood platform has a perimeter which is 8 times the length of a side, decreased by 12. Find the length of a side.

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