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, start superscript, 2, end superscript, plus, 100, w what is the maximum area possible?

Answer 1

2500 meters

Explanation:

Answer 2

Area a(w)=
`-w^2+100w` where w is the width

Area is in quadratic form.

To find maximum are we need to find the vertex.

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

To find vertex we use formula w=
`(-b)/(2a)`

a= -1 and b = 100

So w =
`(-100)/(2(-1))` = 50

We will get maximum area when width w= 50m

To find maximum are we plug in 50 for w and find a(50)

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

a(50)=
`-50^2+100(50)`

a(50)= -2500 + 5000

= 2500

So maximum area is 2500 square meter and the dimensions are length = 50m , width = 50m