You have 500-foot roll of fencing and a large field. You want to construct a rectangular playground area. What are the dimensions of the largest such yard? What is the largest area?

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Answer 1 · 2015-09-26T00:39:20

Refer to explanation

Let #x,y# the sides of a rectangle hence the perimeter is

#P=2*(x+y)=>500=2*(x+y)=>x+y=250#

The area is

#A=x*y=x*(250-x)=250x-x^2#

finding the first derivative we get

#(dA)/dx=250-2x# hence the root of the derivative gives us the maximum value hence

#(dA)/dx=0=>x=125#

and we have #y=125#

Hence the largest area is #x*y=125^2=15,625 # ft^2

Obviously the area is a square.