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?

Area a(w)= where w is the width

Area is in quadratic form.

To find maximum are we need to find the vertex.

a(w)=

To find vertex we use formula w=

a= -1 and b = 100

So w = = 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)=

a(50)=

a(50)= -2500 + 5000

= 2500

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

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step-by-step explanation:

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