what is the maximum area of a rectangle with a fixed perimeter of 130?

Answer 1

OK

If perimeter =130, then 2w + 2L = 130. Now I won't go into the detail of calculus, but let's just say to achieve the maximum area of a rectangle you will see that the sides get closer and closer to being equal. So

2w = 2L so

4s =130 at max point
s (w or l) = 32.5

Now we have both sides - area =
32.5 x 32.5=
1056.25

Hope that helps.

Answer 2

x+y=65 and max of z= x*y
z= x((65-x)= 65x-x^2
z¨=65-2x=0 so x= 32.5 and y =32.5 (a square)

Answer 3

each side is 32.5 for an area of 1056.25