A rancher has set out to fence off two adjacent rectangular pastures for her horses $($as pictured below$).$ She has $2250$ feet of fencing to fence off as large an area as possible. She wants to give the horses barn access, so she is building the pasture along the side of her barn, which will not need fencing.

$($a$)$ Write a function, $A(x),$ that describes the area of the pasture as a function of its length $($the long side$),x.($Don$\text{'}$t need Python for this.$)$

$($b$)$ Plot a graph of $A(x)$ for all practical values of $x.$

$($c$)$ Calculate the dimensions of the largest area with the given restrictions.

$($d$)$ In Calculus, you will learn $($or review$)$ how to find maximum and minimum values by taking the derivative $($diff$)$ of the function and setting it equal to zero $($solve$).$ Use this idea and these commands to verify the dimensions that you found in part $($c$).$