Answer: Dimensions are 800 by 800
Area = 640,000
Step-by-step explanation:
Let the length be x and the width be y
The perimeter of a rectangle is give as ; 2 ( L + B) , that is
2(x+y) = 3200
divide through by 2 , we have
x + y = 3200/2
x + y = 1600
Making y the subject of formula , we have
y = 1600 - x
Let the are of the rectangle be A , then
A = xy
substitute the value of y into A , we have
A = x ( 1600 - x)
A = 1600x - [tex]x^{2}[/tex]
Since we are maximizing, we will find the derivative of A with respect to x , we have
[tex]\frac{dA}{dx}[/tex] = 1600 - 2x
set [tex]\frac{dA}{dx}[/tex] to zero ,
1600 - 2x = 0
1600 = 2x
Therefore x =800
substitute the value of x = 800 into y , we have
y = 1600 - 800
y = 800
The dimensions are 800 by 800
The maximum area is therefore 800 x 800 = 640,000
