Question 31294: please help me with this question i dont understand it at all. find the dimensions of a rectangle a with the greatest area whose perimeter is 30 feet.thank you so much.
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! The perimeter is 30 feet
Call the perimeter p
p = 30
I want to maximize the area
What if the rectangle is a square?
Then the 4 sides are:
7.5, 7.5, 7.5, 7.5
The sides add up to 30, so p = 30 as it should
What's the area? Call it a
a = 7.5 * 7.5 = 56.25
Suppose I change the square just a little
Subtract .5 from two opposite sides and add .5
to the other two opposite sides
Now I have
7, 7, 8, 8
They add up to 30 as they should
a = 7 * 8 = 56
If I try other numbers for sides that add up to 30
6, 6, 9, 9
a = 6 * 9 = 54
The longer and narrower I make the rectangle, the area
keeps getting smaller, so the square with a = 56.25
is the largest area I can get with perimeter = 30
(or any size perimeter, for that matter)
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