Find the dimensions of a rectangle with perimeter 1000 metres so that the area of the rectangle is a maximum.

Dear student

perimeter of rectangle = 2(length+breadth)=1000

let length=x, then breadth = 500-x

Area = x*(500-x)

A=x(500-x)=500x-x2dAdx=500-2xdAdx=0 or 500-2x=0 or x=250d2Adx2=-2so area is maximumarea =250*(500-250)=62500

Regards

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sides= 249, 251 area=62499
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Sides=249 & 251
Area=249×251msq.
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