A rectangular enclosure is to be built for an animal. Zookeepers have 24 meters of fencing, but they want to maximize the area of the enclosure. Let \( x \) be the width of the enclosure. Form an expression for the length of the enclosure in terms of \( x \). length =

To maximize the area of the rectangular enclosure, we start with the total fencing available, which is 24 meters. The perimeter \( P \) of a rectangle is given by the formula \( P = 2L + 2W \). With \( x \) as the width and \( L \) as the length, we can rearrange this to solve for length, giving us the expression \( L = 12 - x \). So now we have our length expressed in terms of the width: \( \text{length} = 12 - x \). Additionally, to find the maximum area, you can use the area formula \( A = L × W \). Substituting the expression for length, the area can be rewritten as \( A = x(12 - x) = 12x - x^2 \). This quadratic function will help you find the dimension that yields the greatest area by using vertex formulas or calculus!