Maximum perimeter of a rectangle with a fixed area
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What is the maximum value of \(P\text{,}\) the length of the perimeter of the rectangle? Find the dimensions of the rectangle of largest area that has its base on the \(x\)-axis and its other two vertices above the \(x\)-axis and lying on the parabola \(y=12-x^2\text{.}\) A farmer has 400 feet of fencing with which to build a rectangular pen.
Best answer Let the length and breadth of rectangle be x and y. If A and P are the area and perimeter of rectangle respectively then Therefore, for largest area of rectangle x=y=P/4 i.e., with given perimeter, rectangle having largest area must be square.