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Answer :
The maximum area is 30000 m².
To find the maximum area of the rectangular part, we need to maximize the length and width of the rectangle while still maintaining a perimeter of 1200 meters.
Let the length of the rectangle be x meters.
The width of the rectangle would then be (600 - 2x) meters, because the total length of the two semicircles is equal to the width of the rectangle.
The area of a rectangle is given by length * width.
Substituting the expressions for length and width, the area becomes:
A = x * (600 - 2x) = 600x - 2x^2
The area is maximized when the derivative of A with respect to x is zero.
Differentiating and setting the derivative equal to zero, we get:
600 - 4x = 0
Solving for x, we find x = 150.
Plugging x = 150 into the area equation, we find the maximum area to be:
A = 150 * (600 - 2 * 150) = 30000 square meters.
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