Suppose you have 52 feet of fencing to enclose a rectangular dog pen. The function A 26x - xwhere x width gives you the area of the dog pen in square feet. What width gives you the maximum area Wha?

To find the width that gives the maximum area, we first express the perimeter constraint. Given that the total Fencing is 52 feet, the relationship between width ( x ) and length ( L ) is ( L = 26 - x ). The area function is ( A = x(26 - x) = 26x - x^2 ). To maximize the area, we can use the vertex formula for a quadratic equation, which occurs at ( x = -\frac{b}{2a} ). Here, ( a = -1 ) and ( b = 26 ), so the maximum area occurs at ( x = 13 ) feet.