Question

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

Answer 1

Answer:

2500 Square meters

Step-by-step 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.