Question 37590
   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.

Yes, use P=2l+2w
400=2l+2w
l+w=200
l=200-w
Now, Area=lw
    A=(200-w)(w)=200w-w^2
Then, w^2-200w+A=0
This is a quadratic with a=1,b=-200, c=A
The maximum is at -b/2a = -(-200)/2=100
So the dimensions are 100' by 100'

Cheers,
Stan H.