Answer: We can start by factoring the given expression for the area of the rectangle:
Area = 144x^2 - 81
Area = (12x)^2 - (9)^2
Area = (12x + 9)(12x - 9)
We can see that the area is expressed as the product of two binomials (12x + 9) and (12x - 9), which represent the length and width of the rectangle, respectively. Therefore:
Length = 12x + 9
Width = 12x - 9
Note that we can check that the product of the length and width indeed equals the area:
Length x Width = (12x + 9)(12x - 9) = 144x^2 - 81 = Area
So, the expressions for the dimensions of the rectangle are:
Length = 12x + 9
Width = 12x - 9
Explanation: