SOLUTION: find the maximum area of a rectangle with a perimeter of 250 feet

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Question 756899: find the maximum area of a rectangle with a perimeter of 250 feet
Answer by sachi(548) About Me  (Show Source):
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perimeter of rectangle with is 250 feet
if the length is x then breadth=250/2-x=125-x
so the area=x[125-x]=125x-x^2=say f(x)
df(x)/dx=d(125x-x^2)/dx=125-2x
so when f(x)is max then the slope df(x)/dx=0
so 125-2x=0
or x=125/2=62.5
so the maximum area=62.5{125-62.5)=3906.25 ft^2