The answer was finding the length and width of a rectangle. The results were x= 3 and x= -4. Neither the length or width can be a negative number. However, 3 did work in the original equation."

You are correct that in a real world physical problem like you cited the answer cannot be negative.

But is the negative answer "extraneous" according to the mathematical definition? Please explain in 2 paragraphs.

The above question must be answered. The question originated from the question below which was already answered: What are extraneous solutions of an equation? Why do they sometimes occur in the process of solving rational or radical equations?