Shenelle has 100 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-25)^2+625. what is the maximum area possible?

Alright, lets get started.

The graden's area is given as :

For maximization of area, a'(w) should be equal to zero.

Simplifying :

w = 25 meters

Fencing is given 100 meters that means that will equal to its perimeter,so

Plugging w as 25

Dividing 2 in both sides

Means for maximum area of rectange, l should be 25 and w should be 25 too.

So, area (maximum) =

Area(maximum) = 625 square meters    :    Answer

Hope it will help :)

625 sq. m.

Step-by-step explanation:

The graden's area is given as :  

For maximization of area,we need to put first order derivative of given equation equals to 0 i.e. a'(w) should be equal to zero.  

On Simplifying :

w = 25 meters

Since we are given that Shenelle has 100 meters of fencing to build a rectangular garden

This means perimeter is equal to 100.

Formula of perimeter of rectangle :

Where l is length

w is width

Plugging w as 25

Dividing 2 in both sides

So, for the maximum area the length should be 25 m and width should 25 m

So, So, maximum area

Hence the maximum possible area is 625 sq. m.

answer:

huuu not sure

step-by-step explanation:

just look it up on the internet i always look it up im sure you will be able to find answers on there

Area as a function of width, w is:
a(w)=(w-25)^2+625
for maximum area, the width will be:
a'(w)=2(w-25)+0=0
solving for w we egt
2w-50=0
2w=50
w=25 m
given that the perimeter is 100, the length will be:
100=2(L+W)
solving for L we get:
L=50-W
but W=25m
hence
L=50-25=25 m
thus the maximum area will be:
A=L*W=25*25=625m^2

The maximum area is 625 square meters.

Step-by-step explanation:

We know that the area is determined by

To find the maxium area, we need to calculate the derivative of this function

Then, we make it equal to zero, to find a maxium value

Now, we solve for

But, according to the problem, the perimeter is 100 meters, because the fencing represents a perimeter.

And,

So,

So, the maxium width is 25 meters, the maxium length is 25 meters, and the maxium area is the product of these dimensions

Therefore, the maximum area is 625 square meters.