Question

A rectangular garden has a perimeter of 120 m. Express its area A as a function of the width w

Answer 1

Answer:

We call x to width and y to high

If perimeter is 120, then  

2 x + 2 y = 120 , or  y = 60 − x

The surface  s ( x ) = x ⋅ y = x ( 60 − x )  is the surface area as function of width

If we want to maximize area, then  s ´ ( x ) = 60 − 2 x = 0

and we obtain as solution  

x = 30

and then the surface will be maximum if rectangle is a square with 30 ft of side

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

Width = w   m

Perimeter = 2 ( Length + Width )  = 120

=> Length + Width = 60

=> Length + w  = 60

=> Length = 60 - w

Area = Length * width

=> Area = (60 - w)w

=> Area = 60w - w²

A =  - w² + 60w

area A as a function of the width w

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area A as a function of the width w

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