Final answer:
The question is about a square with an area represented by a binomial expression, 64 - 16x x^2 square meters. To find the side length, we compare this to the area formula of a square, A = a². The side length is deduced to be 8 - 4x.
Step-by-step explanation:
The question involves a student having a square with an area expressed as a binomial, 64 - 16x x^2 square meters. To solve this problem, we need to understand the relationship between the sides of a square and its area. The area of a square is given by the equation A = a², where A is the area and a is the length of one side. Comparing this with the given expression, we can deduce that the binomial represents a perfect square trinomial.
If we write the given area in the form (a - bx) (a - bx), we are essentially finding the side length of the square. The square of the side length will then give us the area of the square. In our case, the expression is already written as a square of a binomial, which implies the side length is 8 - 4x, since (8 - 4x)² = 64 - 16x x^2.