SOLUTION: Again please help. 4) Amanda has 400 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). She wants to maximize the a

Question 35607: Again please help.
4) Amanda has 400 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). She wants to maximize the area of her patio (area of a rectangle is length times width). What should the dimensions of the patio be, and show how the maximum area of the patio is calculated from the algebraic equation.
Answer:
Show work in this space.

Answer by Paul(988) (Show Source): You can put this solution on YOUR website!
LEt the length be x
Let the width be w
Now 2x+2w=400
SO l=200-w (subsitution)
Use calculus to solve this problem.
Now I will only give you the answer, try to find the critical points, domain, etc by yourself.
Let the area be A:
SO:
xw=A
Subsitute for l:
(200-w)(w)=A
A=w^2-200w
Differentate with respect to w
A'=2w-200
2w=200
w=100
x=200-100
x=100
Henc,e the length is 100 and the width is 100
and the area is 100^2.
Paul.
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