What is the longest strip length that allows both fabrics to be fully utilized explain your reasoning
The longest strip length that allows both fabrics to be fully utilized would be equal to the greatest common divisor (GCD) of the lengths of the two fabrics.
To explain the reasoning, let's consider two fabrics with lengths of 12 yards and 20 yards. The GCD of 12 and 20 is 4 yards. This means that if we cut strips of fabric with a length of 4 yards, we can evenly divide both fabrics and fully utilize them without any leftover fabric.
For example, if we cut three 4-yard strips from the 12-yard fabric, we would use a total of 12 yards. Similarly, if we cut five 4-yard strips from the 20-yard fabric, we would use a total of 20 yards. Therefore, both fabrics would be fully utilized.
If we were to cut longer strip lengths than the GCD, there would always be some leftover fabric that cannot be used efficiently. In this case, if we cut a 5-yard strip instead, we would be left with 2 yards of unused fabric from the 12-yard roll and 15 yards from the 20-yard roll. Thus, cutting strips equal to the GCD ensures maximum utilization of both fabrics.