Question

Marquise has 200200200 meters of fencing to build a rectangular garden.

The garden's area (in square meters) as a function of the garden's width www (in meters) is modeled by:
A(w)=-w^2+100wA(w)=−w
2
+100wA, left parenthesis, w, right parenthesis, equals, minus, w, squared, plus, 100, w
What is the maximum area possible?

Answer 1

2500 Square meters

Explanation:

Given the garden area (as a function of its width) as:

`A(w)=-w^2+100w`

The maximum possible area occurs when we maximize the area. To do this, we take the derivative, set it equal to zero and solve for w.

A'(w)=-2w+100

-2w+100=0

-2w=-100

w=50 meters

Since Marquise has 200 meters of fencing to build a rectangular garden,

Perimeter of the proposed garden=200 meters

Perimeter=2(l+w)

2(l+50)=200

2l+100=200

2l=200-100=100

l=50 meters

The dimensions that will yield the maximum area are therefore:

Length =50 meters

Width=50 meters

Maximum Area Possible =50 X 50 =2500 square meters.