The area of a rectangular park is given by the algebraic expression 6xy. What are the possible expressions for the dimensions of the park?

To determine the possible expressions for the dimensions of the rectangular park given by the area expression 6 x y , we need to think about the properties of rectangles and algebraic expressions.

Understanding the Area Formula : For a rectangle, the area A is calculated as the product of its length l and width w , given by the formula:
A = l × w
In this problem, the area of the rectangle is 6 x y .

Factorization : We need to find pairs of factors of 6 x y that can represent the length and width of the rectangle. Since multiplication is commutative, if l × w = 6 x y , then w × l = 6 x y as well.

Possible Pairs of Factors :

1 × 6 x y and 6 x y × 1
2 × 3 x y and 3 x y × 2
3 × 2 x y and 2 x y × 3
6 × x y and x y × 6

Each of these is a valid pair of dimensions for the length and width of the rectangle.

Assignment of Variables : Generally, either l = f ( x ) and w = g ( x ) or vice versa. So, the expressions for the length and width are flexible as long as their product results in 6 x y .


In conclusion, the area formula 6 x y can result in multiple sets of dimensions for the length and width. These dimensions reflect the flexibility of distributing the factors of an algebraic expression across different terms.

Answered by danjohnbrain | 2025-07-21