The area of a rectangular athletic field is represented by the expression 16y²-49z² 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.
Area = 16y²-49z² = (4y)²-(7z)²
Factorize to get
(4y+7z)(4y-7z).
Can you take it from here?
To find the algebraic expression representing one possible set of dimensions of the athletic field, we need to find the factors of the given expression 16y²-49z².
The given expression can be factored as (4y+7z)(4y-7z) using the difference of squares formula.
Therefore, one possible set of dimensions of the athletic field can be (4y+7z) meters in length and (4y-7z) meters in width.
So, the algebraic expression representing the dimensions of the athletic field is (4y+7z)(4y-7z) square meters.