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?
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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
You can put this solution on YOUR website! The formula for perimeter is
given: cm
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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.
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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
