(Solved): 3. A farmer plans to make two identical and adjacent rectangular pens against a barn (one pen for s ...

3. A farmer plans to make two identical and adjacent rectangular pens against a barn (one pen for sheep, the other for pigs), each with the same area. He has 48 feet of fencing to make the pens. a) Sketch a picture of the pens against the barn and label the width of the pens \( x \) and the length of the pens \( y \) (the fencing that is perpendicular to the barn is the width, the fencing that is parallel to the barn is the length). b) Write a quadratic function \( A(x) \) that represents the area of one of the pens (not the total area combined) in terms of the pens' width \( x \). Write your function in STANDARD FORM. c) Graph your function \( A(x) \) using a graphing calculator or Desmos. What does the point (4, 72) tell us? What does the vertex of the parabola tell us? d) Using algebra, find the dimensions (length and width) of the pens that maximize the possible area given the amount of fencing. What is the maximum area of each pen? Check your answer by looking at the graph of \( A(x) \).