To find the maximum length of a square piece that can be cut from a rectangular piece of paper without any wastage, we need to determine the greatest common divisor (GCD) of the two dimensions of the rectangle (96 cm and 84 cm).
The GCD will represent the side length of the largest square that can be evenly divided from both dimensions.
Using the Euclidean algorithm, we can find the GCD as follows:
Step 1: Divide the larger number (96 cm) by the smaller number (84 cm).
96 ÷ 84 = 1 remainder 12
Step 2: Replace the larger number with the remainder obtained (84 cm) and divide the previous remainder (12 cm) by the new number.
84 ÷ 12 = 7 remainder 0
Step 3: Since the remainder is 0, we stop here.
The GCD is the last non-zero remainder obtained, which is 12 cm.
Therefore, the maximum length of a square piece that can be cut from the rectangular paper without wastage is 12 cm.