Answer:
.Algebraically, we can show that the maximum area of the rectangle is achieved when it is a square. In this case, the maximum area is
Algebraically, we can show that the maximum area of the rectangle is achieved when it is a square. In this case, the maximum area is 400 ft 2
Step-by-step explanation:
Since this is not in calculus, I'll provide a non-calculus answer.
We know the rectangle always has a perimeter of
80, so 2l+2w=80, which simplifies to be +w=40.
We also know that the area of the rectangle is A=lw, but we can express this as a function of a single variable.
Use the perimeter expression l+w=40to say that =40−w Because this will always be true in the rectangle, we can substitute 40−w for l in A=lw.
A=lw
A=(40−w)w
A=-w2+40w
