Answer :
11,250 feet² is the largest total area.
Describe Area?
The region enclosed by an object's shape is referred to as the area.
The area of the shape is the area that the figure or any other two-dimensional geometric shape occupies in a plane.
Let x, y are length and width of the total area .
Given that there is 600 feet of fence to enclose it.
600 = x + x + y + y + y + y
600 = 2x + 4 y
600 = 2 ( x + 2y )
300 = x + 2y
area of the field A = Length * width
A = xy
A = ( 300 - 2Y ) Y
A = 300y - 2y²
A' = d/dy (A)
= d/dy ( 300y - 2y² )
= 300 (1) - 2 (2y)
= 300 - 4y ..................2
also A'' = d/dy(A') = d/dy ( 300 - 4y ) .............. from 2
= 0 - 4 (1)
A'' = 4 ....................3
Take A' = 0
300 - 4y = 0
300 = 4y
y = 75
also at y = 75 , A'' = - 4
< -4
at y = 75, A' = 0 , A'' < 0
By second derivative test A hAS MAX VALUE
When y = 75
also x = 300 - 2y
x = 300 - 2 * 75
x = 300 - 150
x = 150
largest area = A ∫x = 150 y = 75
= 150 * 75
= 11,250 feet²
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