Answer: 
Step-by-step explanation:
1. You know that the force<em> F</em> varies directly as the weight <em>w</em> of the sofa. Then, you can write the following expression:

Where <em>k </em>is the constant of proportionality.
2. You know that a person can push a 120 pound sofa with a force of 50 pounds, then you can calcualte the constant of proportionality as following:

3. Then, the equation is:

The straight length is 5. Use the Pythagorean theorem. a^2+b^2=c^2
We will assume A×B = B×A and show that A and B are necessarily the same.
Assume A×B = B×A. Let a ∈ A and b ∈ B. Then (a,b) ∈ A×B. Since A×B = B×A, we have (a,b) ∈ B×A. That is, a ∈ B and b ∈ A. Therefore, a ∈ A implies a ∈ B and b ∈ B implies b ∈ A. So A = B, as we had set out to do.