Question

Marquises has 200 meters of fencing to build a rectangular garden. The gardens area (in square meters) as a function of the garden's width is (in meters) is modeled by A(W)=-w^2+100w What side width will produce the maximum garden area ?

Answer 1

Answer:50

Step-by-step explanation:

Answer 2

The width of 50 meter will produce the maximum garden area

Solution:

Given that,

$A(w) = -w^2 + 100w$

Where, "w" is the width

Given area is in quadratic form

To find maximum area, we need to find the vertex

$w = \frac{-b}{2a}$

From given quadratic,

$-w^2 + 100w$

a = - 1

b = 100

Therefore,

$w = \frac{-100}{2 \times -1}\\\\w = 50$

We will get maximum area when width w = 50 meters

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

$A(50) = -(50)^2 + 100(50)\\\\A(50) = -2500 + 5000\\\\A(50) = 2500$

So maximum area is 2500 square meter