Respuesta :
The width of 50 meter will produce the maximum garden area
Solution:
Given that,
[tex]A(w) = -w^2 + 100w[/tex]
Where, "w" is the width
Given area is in quadratic form
To find maximum area, we need to find the vertex
[tex]w = \frac{-b}{2a}[/tex]
From given quadratic,
[tex]-w^2 + 100w[/tex]
a = - 1
b = 100
Therefore,
[tex]w = \frac{-100}{2 \times -1}\\\\w = 50[/tex]
We will get maximum area when width w = 50 meters
To find maximum are we plug in 50 for w and find A(50)
[tex]A(50) = -(50)^2 + 100(50)\\\\A(50) = -2500 + 5000\\\\A(50) = 2500[/tex]
So maximum area is 2500 square meter
