Answer:
The  dimensions are x =20 and y=20 of the garden that will maximize its area is 400
Step-by-step explanation:
Step 1:-
let 'x' be the length  and the 'y' be the width of the rectangle
given Jenna's buys 80ft of fencing of rectangle so the perimeter of the rectangle is    2(x +y) = 80 
                          x + y =40 
                                y = 40 -x
now the area of the rectangle A = length X width
                                                   A = x y
substitute 'y' value in above A = x (40 - x) 
                                               A = 40 x - x^2 .....(1)
<u>Step :2</u>
now differentiating equation (1) with respective to 'x'
                                        ........(2)
     ........(2)
<u>Find the dimensions</u>
<u></u> <u></u>
<u></u>
40 - 2x =0
40 = 2x
x = 20
and y = 40 - x = 40 -20 =20
The dimensions are x =20 and y=20
length = 20 and breadth = 20
<u>Step 3</u>:-
we have to find maximum area
Again differentiating equation (2) with respective to 'x' we get

Now the maximum area A =  x y at x =20 and y=20
                                         A = 20 X 20 = 400
                                           
<u>Conclusion</u>:-
The  dimensions are x =20 and y=20 of the garden that will maximize its area is 400
<u>verification</u>:-
The perimeter = 2(x +y) =80
                            2(20 +20) =80
                               2(40) =80
                               80 =80