What is the largest possible area that Lemuel could enclose with the fence, if he wants to enclose a rectangular plot of land with 24 feet of fencing?

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Answer 1 · 2018-03-26T12:01:18

Largest possible area is #36# sq.ft with sides #x=y=6# ft

Let the sides of rectangle is #x and y#

Perimeter of the rectangle is #P=2(x+y)=24 #or

#P= (x+y)=12 :. y=12-x#

Area of the rectangle is #A=x*y= x(12-x)# or

#A= -x^2+12x = -(x^2-12x)# or

#A= -(x^2-12x+36)+36# or

#A= -(x-6)^2+36# . square is non negative quantity.

Therefore to maximize #A# minimum should be deducted from

#36; :. (x-6)^2=0 or x-6=0:. x=6:. A=36 # So largest

possible area is #36# sq.ft with sides #x=y=6# [Ans]