This is a stupid question. The teacher who asked this needs to go back to school.
A = x⁴ - 9y²
That's going to be a number. As long as it's positive we can choose any length for our rectangle L and we can compute the width by W=A/L. So the correct answer is the dimensions are L by (x⁴ - 9y²)/L.
They don't want the correct answer. They want you to factor this expression. We'll do it, but don't believe for a second this factoring somehow constrains the possible dimensions of some rectangle.
We use the difference of two squares, a²-b² = (a+b)(a-b)
A = x⁴ - 9y² = (x²)² - (3y)² = (x²+3y)(x²-3y)
Answer: x²+3y by x²-3y