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]