A rectangular pen is built with one side against a barn. Find the dimensions of the pen that will maximize the enclosed area if the pen has a total length of $1900$ m $.$

Let $\backslash ($ A $\backslash )$ be the area of the rectangular pen and let $\backslash ($ x $\backslash )$ be the length of the sides perpendicular to the barn. Write the function to be optimized in a form that does not include the length of the side parallel to the barn.

$\backslash [$

A$=$

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