The area of a rectangular athletic field is represented by the expression 81y^2-16z^2 square meters. Write an algebraic expression to represent one possible set of dimensions(in the sense " length times width") of the athletic field. Include correct units with your solution.

all you need is a set of factors of the expression

how about
81y^2 - 16z^2 = (9y+4z)(9y-4z)

make one the length, the other the width.

To represent the area of a rectangular athletic field using the expression 81y^2-16z^2 square meters, we need to find a pair of factors that, when multiplied together, result in that expression.

The given expression can be rewritten as (9y)^2 - (4z)^2 square meters. This is a difference of squares, which gives us the formula (a^2 - b^2) = (a + b)(a - b).

Using this, we can determine that the possible dimensions of the athletic field are (9y + 4z) meters for the length and (9y - 4z) meters for the width.

Therefore, the algebraic expression to represent one possible set of dimensions of the athletic field is (9y + 4z) meters by (9y - 4z) meters.