## 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 w

Question

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?

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5 months 2021-08-25T08:08:59+00:00 2 Answers 20 views 0

625 metres

Step-by-step explanation:

Given the area function expressed as a(w)=-(w-25)^2+625.

The maximum area occurs at when da/dw = 0

da/dw = -2(w-25)

0 = -2(w-25)

-2(w-25) = 0

w – 25  = 0

w = 25

Substitute w = 25 into the modeled equation;

Recall a(w)=-(w-25)^2+625.

a(25)=-(25-25)^2+625

a(25) = 0+625

a(25) = 625

Hence the maximum area possible is 625 metres