SOLUTION: If a rectangle with length L and width W has a perimeter of 4 cm, what are the definitions of the rectangle with the largest area and what is that area?

Question 628179: If a rectangle with length L and width W has a perimeter of 4 cm, what are the definitions of the rectangle with the largest area and what is that area?
Found 2 solutions by dfrazzetto, josmiceli:
Answer by dfrazzetto(283) (Show Source): You can put this solution on YOUR website!

Largest possible area of a rectangle is always a square, so L=W
4 = 4L = 4W; L = 1, W = 1
Length = Width = 1cm
Area = LxW = 1x1 = 1 cm^2

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The formula for perimeter is

given:
cm

------------
The formula for area is

By substitution:

This is a parabola with plotted on the
vertical axis and on the horizontal.
The minus sign in front of means
the parabola has a maximum, not a minimum.
------------------------------------
If the equation has the form ,
then the coordinate of the maximum is at

So, the max is at ( 1,A ) where is

The maximum area is 1 cm2
and, if , then

So the maximum area is when the rectangle is a square
with

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