Largest pen against a river

MediumCalculus~4m

You have $200$ metres of fencing to build a rectangular pen along a straight river. The river forms one full side, so no fence is needed there - fencing covers only the other three sides. What is the largest area (in square metres) you can enclose?

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The river side is free: $2x + y = 200$ , so $y = 200-2x$ .
Maximise $A = x(200-2x)$ .

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5000

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Largest pen against a river

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