Respuesta :
Answer:
10,000 ft^2
Step-by-step explanation:
Let x represent length alongside Jane’s house and y represent width of garden.
We have been given that Jana has 200 feet of fencing to enclose a rectangular vegetable garden. One side of the garden will be alongside Jane’s house so only three sides will need to be fenced.
The fencing on 3 sides of garden will be equal to perimeter of garden on three sides.
p = x + 2y
200 = x + 2y
We know that area of rectangle is equal to length times width that is A = xy .
From perimeter equation, we will get:
x = 200 - 2y
Substituting this value in area equation, we will get:
A(y) = (200-y)y
Now, we need to find derivative of area of function.
A(y) = 200y - y^2
A'(y) = 200 - 2y
Now, we will set derivative equal to 0 to find critical points.
200 - 2y = 0
200 = 2y
y = 100
So thus the area will be maximum when 100.
A(y) = 200y - y^2
Substituting y for 100 we get A(100) = 10,000
