SOLUTION: a rectangle has a perimeter of 100 cm what is the length and width if the rectangle is to have the largest possible area

Question 505917: a rectangle has a perimeter of 100 cm what is the length and width if the rectangle is to have the largest possible area
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The largest area for a given perimeter is always a square,
but you can prove it
let the vertical side =
Let the horizontal side =
If the perimeter is ,
and the area is

(1)

Since the coefficient of the squared term is negative
this curve has a maximum, not a minimum.
The vertex is at

and, since

So the sides are all 25 cm and the max area is a square
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