Final answer:
To determine the unknown length of a rectangle with a width of 4 feet and an area of 12x + 24, divide the area by the width, resulting in a length expression of 3x + 6 feet.
Step-by-step explanation:
To find the unknown length of a rectangle when given the width and the area expressed as an algebraic expression, we will use the formula for the area of a rectangle, which is Area = length × width. In this case, the width is 4 feet and the area is given as 12x + 24. To find the length, we divide the area by the width:
Length = Area / Width = (12x + 24) / 4
When we perform the division, each term in the area expression should be divided by the width:
Length = (12x / 4) + (24 / 4)
Length = 3x + 6
Therefore, the unknown length of the rectangle is 3x + 6 feet.