You have 1900 feet of fencing to enclose a rectangular playground and subdivide it into two smaller playgrounds by placing the fencing parallel to one of the sides, as shown in the figure. Express the area of the playground, $A$, as a function of one of its dimensions, $x$. \[ A(x)= \] (Simplify your answer.)

Step 1 ：Let's denote the length of the rectangle as \(x\) and the width as \(y\).

Step 2 ：The total length of the fencing is the sum of the lengths of all sides of the rectangle and the length of the subdivision, which is also \(x\). So, we have the equation \(2x + 3y = 1900\).

Step 3 ：We need to express the area of the playground, \(A\), as a function of one of its dimensions, \(x\). The area of a rectangle is given by the product of its length and width, so \(A = xy\).

Step 4 ：We can solve the equation for \(y\) and substitute it into the area function to express \(A\) as a function of \(x\).

Step 5 ：Solving the equation for \(y\) gives us \(y = \frac{1900}{3} - \frac{2x}{3}\).

Step 6 ：Substituting \(y\) into the area function gives us \(A(x) = x\left(\frac{1900}{3} - \frac{2x}{3}\right)\).

Step 7 ：Simplifying this expression gives us \(A(x) = \frac{1900x}{3} - \frac{2x^2}{3}\).

Step 8 ：Final Answer: \(\boxed{A(x) = \frac{1900x}{3} - \frac{2x^2}{3}}\)