Final answer:
The side length of the new square is 7/3 inches (approximately 2 1/3 inches).
Step-by-step explanation:
To find the side length of the new square, multiply the side length of the original square by the scale factor. The scale factor is 2/3, so the side length of the new square is (3 1/2 inches) * (2/3) = 7/2 inches * 2/3 = 14/6 inches.
Next, simplify the fraction. 14/6 inches simplifies to 7/3 inches.
Therefore, the side length of the new square is 7/3 inches (approximately 2 1/3 inches).